Mudanças entre as edições de "Análise espectral e estabilidade"

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m (→‎Condição de Dirichlet em todos os lados)
m (→‎Condição de Neumann em 3 lados fixando P=1 na entrada (ou na saída))
Linha 602: Linha 602:
 
O espectro tem a maioria dos autovalores próximos do eixo real com alguns autovalores complexos (um pequeno circulo de valores complexos dentro do círculo unitário) com σ ⊂ 11.26 ∪ (-1,1) incluindo 0.
 
O espectro tem a maioria dos autovalores próximos do eixo real com alguns autovalores complexos (um pequeno circulo de valores complexos dentro do círculo unitário) com σ ⊂ 11.26 ∪ (-1,1) incluindo 0.
  
−
Incluindo CC na matriz                  Excluindo CC na matriz
+
  lambda(1)=  1.00000000000000        lambda(1)=  0.955274744954830
−
lambda(1)=  11.2617565379434          lambda(1)=  0.955274744954830
+
  lambda(n)=  0.000000000000000E+000   lambda(n)=  4.218228659674831E-003
−
lambda(n)=  0.000000000000000E+000     lambda(n)=  4.218228659674831E-003
+
      Eigenvalues                          Eigenvalues                   
−
  (<font color="#ff0000"><b>11.262E+00</b></font>, 0.0      )                 (-0.955E+00, 0.0      )
+
  ( 0.100E+01, 0.000E+00)            
−
  ( 0.975E+00, 0.0      )                 ( 0.955E+00, 0.0      )
+
( 0.100E+01, 0.000E+00)            
−
  ( 0.964E+00, 0.0      )                 (-0.896E+00, 0.0      )
+
  ( 0.100E+01, 0.000E+00)            
−
  (-0.948E+00, 0.0      )                 ( 0.896E+00, 0.0      )
+
( 0.100E+01, 0.000E+00)            
−
  ( 0.932E+00, 0.0      )                 ( 0.884E+00, 0.0      )
+
  ( 0.100E+01, 0.000E+00)            
−
  ( 0.920E+00, 0.0      )                (-0.884E+00, 0.0      )
+
( 0.100E+01, 0.000E+00)            
−
  (-0.883E+00, 0.0      )                 ( 0.825E+00, 0.0      )
+
  ( 0.100E+01, 0.000E+00)            
−
  ( 0.877E+00, 0.0      )                 (-0.825E+00, 0.0      )
+
( 0.100E+01, 0.000E+00)            
−
  (-0.861E+00, 0.0      )                 (-0.803E+00, 0.0      )
+
  ( 0.100E+01, 0.000E+00)            
−
  ( 0.836E+00, 0.0      )                 ( 0.803E+00, 0.0      )
+
( 0.100E+01, 0.000E+00)            
−
  ( 0.834E+00, 0.0      )                 ( 0.774E+00, 0.0      )
+
  ( 0.100E+01, 0.000E+00)            
−
  (-0.796E+00, 0.0      )                 (-0.774E+00, 0.0      )
+
  ( 0.994E+00, 0.000E+00)               (-0.955E+00, 0.000E+00)
−
  ( 0.790E+00, 0.0      )                 ( 0.732E+00, 0.0      )
+
  ( 0.964E+00, 0.000E+00)               ( 0.955E+00, 0.000E+00)            
−
  (-0.782E+00, 0.0      )                 (-0.732E+00, 0.0      )
+
  ( 0.950E+00, 0.000E+00)               (-0.896E+00, 0.000E+00)            
−
  ( 0.750E+00, 0.0      )                 ( 0.715E+00, 0.0      )
+
  (-0.948E+00, 0.000E+00)               ( 0.896E+00, 0.000E+00)            
−
  ( 0.750E+00, 0.0      )                 (-0.715E+00, 0.0      )
+
  ( 0.920E+00, 0.000E+00)               ( 0.884E+00, 0.000E+00)            
−
  ( 0.744E+00, 0.0      )                 ( 0.683E+00, 0.0      )
+
  (-0.883E+00, 0.000E+00)               (-0.884E+00, 0.000E+00)            
−
  (-0.728E+00, 0.0      )                 (-0.683E+00, 0.0      )
+
  ( 0.877E+00, 0.000E+00)               ( 0.825E+00, 0.000E+00)            
−
  ( 0.720E+00, 0.0      )                 (-0.634E+00, 0.0      )
+
  ( 0.867E+00, 0.000E+00)               (-0.825E+00, 0.000E+00)            
−
  ( 0.700E+00, 0.0      )                 ( 0.634E+00, 0.0      )
+
  (-0.861E+00, 0.000E+00)               (-0.803E+00, 0.000E+00)            
−
  (-0.695E+00, 0.0      )                 ( 0.621E+00, 0.0      )
+
  ( 0.836E+00, 0.000E+00)               ( 0.803E+00, 0.000E+00)            
−
  (-0.663E+00, 0.0      )                 (-0.621E+00, 0.0      )
+
  ( 0.834E+00, 0.000E+00)               ( 0.774E+00, 0.000E+00)            
−
  (-0.653E+00, 0.0      )                 ( 0.612E+00, 0.0      )
+
  (-0.796E+00, 0.000E+00)               (-0.774E+00, 0.000E+00)            
−
  ( 0.633E+00, 0.0      )                 (-0.612E+00, 0.0      )
+
  (-0.782E+00, 0.000E+00)               ( 0.732E+00, 0.000E+00)            
−
  ( 0.617E+00, 0.0      )                 ( 0.575E+00, 0.0      )
+
  ( 0.750E+00, 0.000E+00)               (-0.732E+00, 0.000E+00)            
−
  ( 0.581E+00, 0.0      )                 (-0.575E+00, 0.0      )
+
  ( 0.750E+00, 0.000E+00)               ( 0.715E+00, 0.000E+00)            
−
  ( 0.581E+00, 0.0      )                 ( 0.547E+00, 0.0      )
+
  ( 0.744E+00, 0.000E+00)               (-0.715E+00, 0.000E+00)            
−
  (-0.566E+00, 0.0      )                 (-0.547E+00, 0.0      )
+
  (-0.728E+00, 0.000E+00)               ( 0.683E+00, 0.000E+00)            
−
  (-0.565E+00, 0.0      )                 ( 0.502E+00, 0.0      )
+
  ( 0.720E+00, 0.000E+00)               (-0.683E+00, 0.000E+00)            
−
  (-0.562E+00, 0.0      )                 (-0.502E+00, 0.0      )
+
  ( 0.700E+00, 0.000E+00)               (-0.634E+00, 0.000E+00)            
−
  ( 0.537E+00, 0.0      )                 ( 0.482E+00, 0.0      )
+
  (-0.695E+00, 0.000E+00)               ( 0.634E+00, 0.000E+00)            
−
  (-0.507E+00, 0.0      )                 (-0.482E+00, 0.0      )
+
  (-0.663E+00, 0.000E+00)               ( 0.621E+00, 0.000E+00)            
−
  ( 0.500E+00, 0.0      )                 ( 0.480E+00, 0.0      )
+
  (-0.653E+00, 0.000E+00)               (-0.621E+00, 0.000E+00)            
−
  (-0.500E+00, 0.0      )                 (-0.480E+00, 0.0      )
+
  ( 0.633E+00, 0.000E+00)               ( 0.612E+00, 0.000E+00)            
−
  ( 0.498E+00, 0.138E-01)                 ( 0.476E+00, 0.0      )
+
  ( 0.617E+00, 0.000E+00)               (-0.612E+00, 0.000E+00)            
−
  ( 0.498E+00,-0.138E-01)                 (-0.476E+00, 0.0      )
+
  ( 0.611E+00, 0.000E+00)               ( 0.575E+00, 0.000E+00)            
−
  ( 0.494E+00, 0.0      )                 ( 0.421E+00, 0.0      )
+
  ( 0.581E+00, 0.000E+00)               (-0.575E+00, 0.000E+00)            
−
  ( 0.453E+00, 0.0      )                 (-0.421E+00, 0.0      )
+
  ( 0.581E+00, 0.000E+00)               ( 0.547E+00, 0.000E+00)            
−
  (-0.433E+00, 0.0      )                 ( 0.404E+00, 0.0      )
+
  (-0.566E+00, 0.000E+00)               (-0.547E+00, 0.000E+00)            
−
  ( 0.432E+00, 0.0      )                 (-0.404E+00, 0.0      )
+
  (-0.565E+00, 0.000E+00)               ( 0.502E+00, 0.000E+00)            
−
  (-0.420E+00, 0.0      )                 ( 0.365E+00, 0.0      )
+
  (-0.562E+00, 0.000E+00)               (-0.502E+00, 0.000E+00)            
−
  ( 0.408E+00, 0.0      )                 (-0.365E+00, 0.0      )
+
  ( 0.537E+00, 0.000E+00)               ( 0.482E+00, 0.000E+00)            
−
  (-0.399E+00, 0.0      )                 ( 0.362E+00, 0.0      )
+
  (-0.507E+00, 0.000E+00)               (-0.482E+00, 0.000E+00)            
−
  (-0.391E+00, 0.0      )                 (-0.362E+00, 0.0      )
+
  ( 0.500E+00, 0.000E+00)               ( 0.480E+00, 0.000E+00)            
−
  ( 0.364E+00, 0.0      )                 (-0.333E+00, 0.0      )
+
  (-0.500E+00, 0.000E+00)               (-0.480E+00, 0.000E+00)            
−
  ( 0.361E+00, 0.0      )                 ( 0.333E+00, 0.0      )
+
  ( 0.494E+00, 0.000E+00)               ( 0.476E+00, 0.000E+00)            
−
  (-0.359E+00, 0.0      )                 ( 0.327E+00, 0.0      )
+
  ( 0.463E+00, 0.000E+00)               (-0.476E+00, 0.000E+00)            
−
  ( 0.346E+00, 0.0      )                 (-0.327E+00, 0.0      )
+
  ( 0.453E+00, 0.000E+00)               ( 0.421E+00, 0.000E+00)            
−
  ( 0.337E+00, 0.0      )                 (-0.325E+00, 0.0      )
+
  (-0.433E+00, 0.000E+00)               (-0.421E+00, 0.000E+00)            
−
  (-0.326E+00, 0.0      )                 ( 0.325E+00, 0.0      )
+
  ( 0.432E+00, 0.000E+00)               ( 0.404E+00, 0.000E+00)            
−
  (-0.287E+00, 0.0      )                 (-0.268E+00, 0.0      )
+
  (-0.420E+00, 0.000E+00)               (-0.404E+00, 0.000E+00)            
−
  ( 0.287E+00, 0.0      )                 ( 0.268E+00, 0.0      )
+
  ( 0.408E+00, 0.000E+00)               ( 0.365E+00, 0.000E+00)            
−
  ( 0.280E+00, 0.0      )                 (-0.266E+00, 0.0      )
+
  (-0.399E+00, 0.000E+00)               (-0.365E+00, 0.000E+00)            
−
  (-0.272E+00, 0.0      )                 ( 0.266E+00, 0.0      )
+
  (-0.391E+00, 0.000E+00)               ( 0.362E+00, 0.000E+00)            
−
  (-0.269E+00, 0.0      )                 ( 0.226E+00, 0.0      )
+
  ( 0.364E+00, 0.000E+00)               (-0.362E+00, 0.000E+00)            
−
  ( 0.247E+00, 0.0      )                 (-0.226E+00, 0.0      )
+
  ( 0.361E+00, 0.000E+00)               (-0.333E+00, 0.000E+00)            
−
  ( 0.244E+00, 0.0      )                 ( 0.223E+00, 0.0      )
+
  (-0.359E+00, 0.000E+00)               ( 0.333E+00, 0.000E+00)            
−
  (-0.228E+00, 0.0      )                 (-0.223E+00, 0.0      )
+
  ( 0.346E+00, 0.000E+00)               ( 0.327E+00, 0.000E+00)            
−
  (-0.225E+00, 0.0      )                 (-0.208E+00, 0.0      )
+
  ( 0.337E+00, 0.000E+00)               (-0.327E+00, 0.000E+00)            
−
  (-0.220E+00, 0.0      )                 ( 0.208E+00, 0.0      )
+
  (-0.326E+00, 0.000E+00)               (-0.325E+00, 0.000E+00)            
−
  ( 0.213E+00, 0.0      )                 ( 0.197E+00, 0.0      )
+
  ( 0.317E+00, 0.000E+00)               ( 0.325E+00, 0.000E+00)            
−
  ( 0.207E+00, 0.0      )                 (-0.197E+00, 0.0      )
+
  (-0.287E+00, 0.000E+00)               (-0.268E+00, 0.000E+00)            
−
  ( 0.200E+00, 0.0      )                 ( 0.186E+00, 0.0      )
+
  ( 0.287E+00, 0.000E+00)               ( 0.268E+00, 0.000E+00)            
−
  ( 0.200E+00, 0.0      )                 (-0.186E+00, 0.0      )
+
  ( 0.280E+00, 0.000E+00)               (-0.266E+00, 0.000E+00)            
−
  ( 0.198E+00, 0.0      )                 ( 0.173E+00, 0.0      )
+
  (-0.272E+00, 0.000E+00)               ( 0.266E+00, 0.000E+00)            
−
  ( 0.163E+00, 0.0      )                 (-0.173E+00, 0.0      )
+
  (-0.269E+00, 0.000E+00)               ( 0.226E+00, 0.000E+00)            
−
  (-0.163E+00, 0.0      )                 ( 0.148E+00, 0.0      )
+
  ( 0.244E+00, 0.000E+00)               (-0.226E+00, 0.000E+00)            
−
  ( 0.158E+00, 0.0      )                 (-0.148E+00, 0.0      )
+
  (-0.228E+00, 0.000E+00)               ( 0.223E+00, 0.000E+00)            
−
  (-0.139E+00, 0.0      )                 ( 0.127E+00, 0.0      )
+
  (-0.225E+00, 0.000E+00)               (-0.223E+00, 0.000E+00)            
−
  (-0.133E+00, 0.0      )                 (-0.127E+00, 0.0      )
+
  (-0.220E+00, 0.000E+00)               (-0.208E+00, 0.000E+00)            
−
  (-0.124E+00, 0.0      )                 (-0.862E-01, 0.0      )
+
  ( 0.213E+00, 0.000E+00)               ( 0.208E+00, 0.000E+00)            
−
  ( 0.117E+00, 0.0      )                 ( 0.862E-01, 0.0      )
+
  ( 0.200E+00, 0.000E+00)               ( 0.197E+00, 0.000E+00)            
−
  ( 0.111E+00, 0.0      )                 (-0.834E-01, 0.0      )
+
  ( 0.200E+00, 0.000E+00)               (-0.197E+00, 0.000E+00)            
−
  (-0.103E+00, 0.0      )                 ( 0.834E-01, 0.0      )
+
  ( 0.198E+00, 0.000E+00)               ( 0.186E+00, 0.000E+00)            
−
  (-0.958E-01, 0.0      )                 (-0.771E-01, 0.0      )
+
  ( 0.188E+00, 0.000E+00)               (-0.186E+00, 0.000E+00)            
−
  (-0.948E-01, 0.0      )                 ( 0.771E-01, 0.0      )
+
  ( 0.163E+00, 0.000E+00)               ( 0.173E+00, 0.000E+00)            
−
  ( 0.713E-01, 0.0      )                 (-0.752E-01, 0.0      )
+
  (-0.163E+00, 0.000E+00)               (-0.173E+00, 0.000E+00)            
−
  ( 0.675E-01, 0.0      )                 ( 0.752E-01, 0.0      )
+
  ( 0.158E+00, 0.000E+00)               ( 0.148E+00, 0.000E+00)            
−
  ( 0.673E-01, 0.0      )                 (-0.712E-01, 0.0      )
+
  (-0.139E+00, 0.000E+00)               (-0.148E+00, 0.000E+00)            
−
  ( 0.668E-01, 0.0      )                 ( 0.712E-01, 0.0      )
+
  (-0.133E+00, 0.000E+00)               ( 0.127E+00, 0.000E+00)            
−
  (-0.617E-01, 0.0      )                 ( 0.549E-01, 0.0      )
+
  (-0.124E+00, 0.000E+00)               (-0.127E+00, 0.000E+00)            
−
  ( 0.567E-01, 0.0      )                 (-0.549E-01, 0.0      )
+
  ( 0.117E+00, 0.000E+00)               (-0.862E-01, 0.000E+00)            
−
  ( 0.495E-01, 0.0      )                 (-0.532E-01, 0.0      )
+
  ( 0.111E+00, 0.000E+00)               ( 0.862E-01, 0.000E+00)            
−
  (-0.301E-01, 0.0      )                 ( 0.532E-01, 0.0      )
+
  (-0.103E+00, 0.000E+00)               (-0.834E-01, 0.000E+00)            
−
  ( 0.246E-01, 0.0      )                 ( 0.335E-01, 0.0      )
+
  (-0.958E-01, 0.000E+00)               ( 0.834E-01, 0.000E+00)            
−
  ( 0.245E-01, 0.0      )                 (-0.335E-01, 0.0      )
+
  (-0.948E-01, 0.000E+00)               (-0.771E-01, 0.000E+00)            
−
  ( 0.244E-01, 0.0      )                 ( 0.161E-01, 0.0      )
+
  ( 0.869E-01, 0.000E+00)               ( 0.771E-01, 0.000E+00)            
−
  (-0.194E-01, 0.0      )                 (-0.161E-01, 0.0      )
+
  ( 0.713E-01, 0.000E+00)               (-0.752E-01, 0.000E+00)            
−
  (-0.165E-01, 0.0      )                 ( 0.422E-02, 0.0      )
+
  ( 0.675E-01, 0.000E+00)               ( 0.752E-01, 0.000E+00)            
−
  (-0.794E-02, 0.0      )                 (-0.422E-02, 0.0      )
+
  ( 0.673E-01, 0.000E+00)               (-0.712E-01, 0.000E+00)            
−
  (-0.568E-08, 0.0      )
+
  (-0.617E-01, 0.000E+00)               ( 0.712E-01, 0.000E+00)            
−
( 0.568E-08, 0.0      )
+
  ( 0.567E-01, 0.000E+00)               ( 0.549E-01, 0.000E+00)            
−
  ( 0.308E-14, 0.0      )
+
  ( 0.495E-01, 0.000E+00)               (-0.549E-01, 0.000E+00)            
−
(-0.178E-14, 0.136E-14)
+
  (-0.301E-01, 0.000E+00)               (-0.532E-01, 0.000E+00)            
−
  (-0.178E-14,-0.136E-14)
+
  ( 0.246E-01, 0.000E+00)               ( 0.532E-01, 0.000E+00)            
−
(-0.126E-14, 0.0      )
+
  ( 0.244E-01, 0.000E+00)               ( 0.335E-01, 0.000E+00)            
−
  ( 0.882E-15, 0.828E-15)
+
  ( 0.222E-01, 0.000E+00)               (-0.335E-01, 0.000E+00)            
−
( 0.882E-15,-0.828E-15)
+
  (-0.194E-01, 0.000E+00)               ( 0.161E-01, 0.000E+00)            
−
  ( 0.518E-15, 0.109E-14)
+
  (-0.165E-01, 0.000E+00)               (-0.161E-01, 0.000E+00)            
−
  ( 0.518E-15,-0.109E-14)
+
  (-0.794E-02, 0.000E+00)              ( 0.422E-02, 0.000E+00)            
−
(-0.466E-16, 0.552E-15)
+
  ( 0.841E-09, 0.000E+00)               (-0.422E-02, 0.000E+00)            
−
  (-0.466E-16,-0.552E-15)
+
  (-0.841E-09, 0.000E+00)
−
  ( 0.508E-15, 0.0      )
+
  (-0.308E-13, 0.000E+00)
−
  (-0.336E-15, 0.361E-15)
+
  ( 0.297E-14, 0.401E-15)
−
  (-0.336E-15,-0.361E-15)
+
  ( 0.297E-14,-0.401E-15)
−
  ( 0.154E-15, 0.417E-15)
+
  (-0.245E-14, 0.000E+00)
−
  ( 0.154E-15,-0.417E-15)
+
  ( 0.124E-14, 0.000E+00)
−
  (-0.333E-15, 0.0      )
+
  (-0.702E-15, 0.693E-15)
−
  (-0.275E-15, 0.112E-15)
+
  (-0.702E-15,-0.693E-15)
−
  (-0.275E-15,-0.112E-15)
+
  ( 0.671E-15, 0.438E-15)
−
  ( 0.156E-15, 0.208E-15)
+
  ( 0.671E-15,-0.438E-15)
−
  ( 0.156E-15,-0.208E-15)
+
  (-0.404E-15, 0.517E-15)
−
  ( 0.253E-16, 0.658E-16)
+
  (-0.404E-15,-0.517E-15)
−
  ( 0.253E-16,-0.658E-16)
+
  ( 0.230E-15, 0.290E-15)
−
  ( 0.666E-16, 0.0      )
+
  ( 0.230E-15,-0.290E-15)
−
  (-0.536E-16, 0.0      )
+
  (-0.317E-15, 0.000E+00)
−
  (-0.205E-16, 0.0      )
+
  (-0.302E-15, 0.000E+00)
−
  (-0.119E-16, 0.0      )
+
  (-0.589E-16, 0.240E-15)
−
  ( 0.259E-18, 0.106E-16)
+
  (-0.589E-16,-0.240E-15)
−
  ( 0.259E-18,-0.106E-16)
+
  (-0.138E-15, 0.790E-16)
−
  (-0.216E-29, 0.0      )
+
  (-0.138E-15,-0.790E-16)
−
  ( 0.171E-29, 0.0      )
+
  ( 0.146E-15, 0.000E+00)
−
  ( 0.357E-30, 0.914E-31)
+
  (-0.599E-16, 0.168E-16)
−
  ( 0.357E-30,-0.914E-31)
+
  (-0.599E-16,-0.168E-16)
−
  (-0.246E-30, 0.0      )
+
  ( 0.309E-16, 0.000E+00)
−
  (-0.204E-31, 0.0      )
+
  ( 0.123E-16, 0.000E+00)
−
  (-0.392E-32, 0.313E-32)
+
  (-0.442E-17, 0.108E-16)
−
  (-0.392E-32,-0.313E-32)
+
  (-0.442E-17,-0.108E-16)
−
  ( 0.0      , 0.0      )
+
  (-0.940E-30, 0.000E+00)
−
  ( 0.0      , 0.0      )
+
  ( 0.000E+00, 0.000E+00)
−
  ( 0.0      , 0.0      )
+
  ( 0.000E+00, 0.000E+00)
−
  ( 0.0      , 0.0      )
+
  ( 0.000E+00, 0.000E+00)
  
 
===Teste 5===
 
===Teste 5===

Edição das 15h22min de 30 de julho de 2009

A análise dos autovalores de uma matriz de iteração pode ser usada para estudar a estabilidade de um método iterativo.

Vamos relatar um estudo para um problema específico.

O problema

Queremos aproximar a solução da equação de Navier Stokes em um duto. Para isso devemos resolver a cada passo de tempo uma equação de Poisson como <math>\frac{\partial^2 p}{\partial x^2}+\frac{\partial^2 p}{\partial y^2}= f(u)\,\!</math>

que é discretizada como

<math>a p_{i+1,j}+a p_{i-1,j}+c p_{i,j} +b p_{i,j+1}+b p_{i,j-1} = f_{i,j} \,\!</math>

  • A matriz possui o estêncil [...b,0...0,a,c,a,0...0,b,0...] onde

<math>a=\frac{-1}{dx^2}, b=\frac{-1}{dy^2}, c=-2a-2a \,\!</math>

  • O espectro do problema não depende de dt, Re ou U0. Depende apenas de a, b e c.
  • Para montar a matriz de iteração corretamente usamos como condição de Dirichlet
 p(contorno) = p0
e dentro do loop de iteração temos
 pnew(contorno)= p(contorno)
ou seja, p continua sempre fixo.

Condição de Dirichlet em todos os lados

Antes de entrar no loop fixamos 

 p( :, 1)= p_sul
 p( :,ny)= p_norte
 p( 1, :)= p_oeste
 p(nx, :)= p_leste

Para obter a matriz de iteração foi necessário usar as CC. 

 pnew( :, 1)= p( :, 1)
 pnew( :,ny)= p( :,ny)
 pnew( 1, :)= p( 1, :)
 pnew(nx, :)= p(nx, :)

O espectro é real com 0<|λ|<1. A condição de contorno contribui com autovalores λ=1. 

 lambda(1)=   1.00000000000000           lambda(1)=  0.955274744954830
 lambda(n)=  4.218228659668808E-003      lambda(n)=  4.218228659674831E-003
      Eigenvalues                             Eigenvalues
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
( 0.100E+01, 0.000E+00)                 
(-0.955E+00, 0.000E+00)                 (-0.955E+00, 0.000E+00)
( 0.955E+00, 0.000E+00)                 ( 0.955E+00, 0.000E+00)
( 0.896E+00, 0.000E+00)                 (-0.896E+00, 0.000E+00)
(-0.896E+00, 0.000E+00)                 ( 0.896E+00, 0.000E+00)
(-0.884E+00, 0.000E+00)                 ( 0.884E+00, 0.000E+00)
( 0.884E+00, 0.000E+00)                 (-0.884E+00, 0.000E+00)
( 0.825E+00, 0.000E+00)                 ( 0.825E+00, 0.000E+00)
(-0.825E+00, 0.000E+00)                 (-0.825E+00, 0.000E+00)
( 0.803E+00, 0.000E+00)                 (-0.803E+00, 0.000E+00)
(-0.803E+00, 0.000E+00)                 ( 0.803E+00, 0.000E+00)
(-0.774E+00, 0.000E+00)                 ( 0.774E+00, 0.000E+00)
( 0.774E+00, 0.000E+00)                 (-0.774E+00, 0.000E+00)
( 0.732E+00, 0.000E+00)                 ( 0.732E+00, 0.000E+00)
(-0.732E+00, 0.000E+00)                 (-0.732E+00, 0.000E+00)
(-0.715E+00, 0.000E+00)                 ( 0.715E+00, 0.000E+00)
( 0.715E+00, 0.000E+00)                 (-0.715E+00, 0.000E+00)
( 0.683E+00, 0.000E+00)                 ( 0.683E+00, 0.000E+00)
(-0.683E+00, 0.000E+00)                 (-0.683E+00, 0.000E+00)
(-0.634E+00, 0.000E+00)                 (-0.634E+00, 0.000E+00)
( 0.634E+00, 0.000E+00)                 ( 0.634E+00, 0.000E+00)
( 0.621E+00, 0.000E+00)                 ( 0.621E+00, 0.000E+00)
(-0.621E+00, 0.000E+00)                 (-0.621E+00, 0.000E+00)
(-0.612E+00, 0.000E+00)                 ( 0.612E+00, 0.000E+00)
( 0.612E+00, 0.000E+00)                 (-0.612E+00, 0.000E+00)
( 0.575E+00, 0.000E+00)                 ( 0.575E+00, 0.000E+00)
(-0.575E+00, 0.000E+00)                 (-0.575E+00, 0.000E+00)
(-0.547E+00, 0.000E+00)                 ( 0.547E+00, 0.000E+00)
( 0.547E+00, 0.000E+00)                 (-0.547E+00, 0.000E+00)
( 0.502E+00, 0.000E+00)                 ( 0.502E+00, 0.000E+00)
(-0.502E+00, 0.000E+00)                 (-0.502E+00, 0.000E+00)
(-0.482E+00, 0.000E+00)                 ( 0.482E+00, 0.000E+00)
( 0.482E+00, 0.000E+00)                 (-0.482E+00, 0.000E+00)
(-0.480E+00, 0.000E+00)                 ( 0.480E+00, 0.000E+00)
( 0.480E+00, 0.000E+00)                 (-0.480E+00, 0.000E+00)
(-0.476E+00, 0.000E+00)                 ( 0.476E+00, 0.000E+00)
( 0.476E+00, 0.000E+00)                 (-0.476E+00, 0.000E+00)
( 0.421E+00, 0.000E+00)                 ( 0.421E+00, 0.000E+00)
(-0.421E+00, 0.000E+00)                 (-0.421E+00, 0.000E+00)
(-0.404E+00, 0.000E+00)                 ( 0.404E+00, 0.000E+00)
( 0.404E+00, 0.000E+00)                 (-0.404E+00, 0.000E+00)
(-0.365E+00, 0.000E+00)                 ( 0.365E+00, 0.000E+00)
( 0.365E+00, 0.000E+00)                 (-0.365E+00, 0.000E+00)
( 0.362E+00, 0.000E+00)                 ( 0.362E+00, 0.000E+00)
(-0.362E+00, 0.000E+00)                 (-0.362E+00, 0.000E+00)
( 0.333E+00, 0.000E+00)                 (-0.333E+00, 0.000E+00)
(-0.333E+00, 0.000E+00)                 ( 0.333E+00, 0.000E+00)
(-0.327E+00, 0.000E+00)                 ( 0.327E+00, 0.000E+00)
( 0.327E+00, 0.000E+00)                 (-0.327E+00, 0.000E+00)
( 0.325E+00, 0.000E+00)                 (-0.325E+00, 0.000E+00)
(-0.325E+00, 0.000E+00)                 ( 0.325E+00, 0.000E+00)
( 0.268E+00, 0.000E+00)                 (-0.268E+00, 0.000E+00)
(-0.268E+00, 0.000E+00)                 ( 0.268E+00, 0.000E+00)
( 0.266E+00, 0.000E+00)                 (-0.266E+00, 0.000E+00)
(-0.266E+00, 0.000E+00)                 ( 0.266E+00, 0.000E+00)
( 0.226E+00, 0.000E+00)                 ( 0.226E+00, 0.000E+00)
(-0.226E+00, 0.000E+00)                 (-0.226E+00, 0.000E+00)
(-0.223E+00, 0.000E+00)                 ( 0.223E+00, 0.000E+00)
( 0.223E+00, 0.000E+00)                 (-0.223E+00, 0.000E+00)
(-0.208E+00, 0.000E+00)                 (-0.208E+00, 0.000E+00)
( 0.208E+00, 0.000E+00)                 ( 0.208E+00, 0.000E+00)
(-0.197E+00, 0.000E+00)                 ( 0.197E+00, 0.000E+00)
( 0.197E+00, 0.000E+00)                 (-0.197E+00, 0.000E+00)
(-0.186E+00, 0.000E+00)                 ( 0.186E+00, 0.000E+00)
( 0.186E+00, 0.000E+00)                 (-0.186E+00, 0.000E+00)
( 0.173E+00, 0.000E+00)                 ( 0.173E+00, 0.000E+00)
(-0.173E+00, 0.000E+00)                 (-0.173E+00, 0.000E+00)
( 0.148E+00, 0.000E+00)                 ( 0.148E+00, 0.000E+00)
(-0.148E+00, 0.000E+00)                 (-0.148E+00, 0.000E+00)
(-0.127E+00, 0.000E+00)                 ( 0.127E+00, 0.000E+00)
( 0.127E+00, 0.000E+00)                 (-0.127E+00, 0.000E+00)
(-0.862E-01, 0.000E+00)                 (-0.862E-01, 0.000E+00)
( 0.862E-01, 0.000E+00)                 ( 0.862E-01, 0.000E+00)
(-0.834E-01, 0.000E+00)                 (-0.834E-01, 0.000E+00)
( 0.834E-01, 0.000E+00)                 ( 0.834E-01, 0.000E+00)
( 0.771E-01, 0.000E+00)                 (-0.771E-01, 0.000E+00)
(-0.771E-01, 0.000E+00)                 ( 0.771E-01, 0.000E+00)
( 0.752E-01, 0.000E+00)                 (-0.752E-01, 0.000E+00)
(-0.752E-01, 0.000E+00)                 ( 0.752E-01, 0.000E+00)
(-0.712E-01, 0.000E+00)                 (-0.712E-01, 0.000E+00)
( 0.712E-01, 0.000E+00)                 ( 0.712E-01, 0.000E+00)
(-0.549E-01, 0.000E+00)                 ( 0.549E-01, 0.000E+00)
( 0.549E-01, 0.000E+00)                 (-0.549E-01, 0.000E+00)
( 0.532E-01, 0.000E+00)                 (-0.532E-01, 0.000E+00)
(-0.532E-01, 0.000E+00)                 ( 0.532E-01, 0.000E+00)
(-0.335E-01, 0.000E+00)                 ( 0.335E-01, 0.000E+00)
( 0.335E-01, 0.000E+00)                 (-0.335E-01, 0.000E+00)
(-0.161E-01, 0.000E+00)                 ( 0.161E-01, 0.000E+00)
( 0.161E-01, 0.000E+00)                 (-0.161E-01, 0.000E+00)
( 0.422E-02, 0.000E+00)                 ( 0.422E-02, 0.000E+00)
(-0.422E-02, 0.000E+00)                 (-0.422E-02, 0.000E+00)

Condição de Neumann em todos os lados

Usando as CC 

 pnew( :,1 ) = pnew(:,2)
 pnew( :,ny) = pnew(:,ny-1)
 pnew( 1,: ) = pnew(2,:)
 pnew(nx,: ) = pnew(nx-1,:)

O espectro é real com σ⊂(-1,1). 

Incluindo CC na matriz                 Eliminando CC na matriz

 lambda(1)=   1.00000000000000          lambda(1)=  0.955274744954830
 lambda(n)=  0.000000000000000E+000     lambda(n)=  4.218228659674831E-003  
      Eigenvalues                            Eigenvalues                    
( 0.100E+01, 0.000E+00)                (-0.955E+00, 0.000E+00)              
( 0.976E+00, 0.000E+00)                ( 0.955E+00, 0.000E+00)              
( 0.970E+00, 0.000E+00)                (-0.896E+00, 0.000E+00)              
(-0.945E+00, 0.000E+00)                ( 0.896E+00, 0.000E+00)              
( 0.945E+00, 0.000E+00)                ( 0.884E+00, 0.000E+00)              
( 0.905E+00, 0.000E+00)                (-0.884E+00, 0.000E+00)              
( 0.883E+00, 0.000E+00)                ( 0.825E+00, 0.000E+00)              
(-0.874E+00, 0.000E+00)                (-0.825E+00, 0.000E+00)              
( 0.874E+00, 0.000E+00)                (-0.803E+00, 0.000E+00)              
( 0.859E+00, 0.000E+00)                ( 0.803E+00, 0.000E+00)              
(-0.859E+00, 0.000E+00)                ( 0.774E+00, 0.000E+00)              
( 0.794E+00, 0.000E+00)                (-0.774E+00, 0.000E+00)              
(-0.788E+00, 0.000E+00)                ( 0.732E+00, 0.000E+00)              
( 0.788E+00, 0.000E+00)                (-0.732E+00, 0.000E+00)              
( 0.764E+00, 0.000E+00)                ( 0.715E+00, 0.000E+00)              
(-0.764E+00, 0.000E+00)                (-0.715E+00, 0.000E+00)              
( 0.750E+00, 0.000E+00)                ( 0.683E+00, 0.000E+00)              
(-0.726E+00, 0.000E+00)                (-0.683E+00, 0.000E+00)              
( 0.726E+00, 0.000E+00)                (-0.634E+00, 0.000E+00)              
( 0.677E+00, 0.000E+00)                ( 0.634E+00, 0.000E+00)              
(-0.677E+00, 0.000E+00)                ( 0.621E+00, 0.000E+00)              
(-0.655E+00, 0.000E+00)                (-0.621E+00, 0.000E+00)              
( 0.655E+00, 0.000E+00)                ( 0.612E+00, 0.000E+00)              
( 0.655E+00, 0.000E+00)                (-0.612E+00, 0.000E+00)              
( 0.624E+00, 0.000E+00)                ( 0.575E+00, 0.000E+00)              
(-0.624E+00, 0.000E+00)                (-0.575E+00, 0.000E+00)              
( 0.587E+00, 0.000E+00)                ( 0.547E+00, 0.000E+00)              
(-0.562E+00, 0.000E+00)                (-0.547E+00, 0.000E+00)              
( 0.562E+00, 0.000E+00)                ( 0.502E+00, 0.000E+00)              
(-0.544E+00, 0.000E+00)                (-0.502E+00, 0.000E+00)              
( 0.544E+00, 0.000E+00)                ( 0.482E+00, 0.000E+00)              
( 0.538E+00, 0.000E+00)                (-0.482E+00, 0.000E+00)              
(-0.538E+00, 0.000E+00)                ( 0.480E+00, 0.000E+00)              
( 0.500E+00, 0.000E+00)                (-0.480E+00, 0.000E+00)              
( 0.491E+00, 0.000E+00)                ( 0.476E+00, 0.000E+00)              
(-0.491E+00, 0.000E+00)                (-0.476E+00, 0.000E+00)              
(-0.470E+00, 0.000E+00)                ( 0.421E+00, 0.000E+00)              
( 0.470E+00, 0.000E+00)                (-0.421E+00, 0.000E+00)              
( 0.413E+00, 0.000E+00)                ( 0.404E+00, 0.000E+00)              
(-0.405E+00, 0.000E+00)                (-0.404E+00, 0.000E+00)              
( 0.405E+00, 0.000E+00)                ( 0.365E+00, 0.000E+00)              
(-0.389E+00, 0.000E+00)                (-0.365E+00, 0.000E+00)              
( 0.389E+00, 0.000E+00)                ( 0.362E+00, 0.000E+00)              
(-0.383E+00, 0.000E+00)                (-0.362E+00, 0.000E+00)              
( 0.383E+00, 0.000E+00)                (-0.333E+00, 0.000E+00)              
(-0.381E+00, 0.000E+00)                ( 0.333E+00, 0.000E+00)              
( 0.381E+00, 0.000E+00)                ( 0.327E+00, 0.000E+00)              
( 0.345E+00, 0.000E+00)                (-0.327E+00, 0.000E+00)              
(-0.318E+00, 0.000E+00)                (-0.325E+00, 0.000E+00)              
( 0.318E+00, 0.000E+00)                ( 0.325E+00, 0.000E+00)              
( 0.315E+00, 0.000E+00)                (-0.268E+00, 0.000E+00)              
(-0.315E+00, 0.000E+00)                ( 0.268E+00, 0.000E+00)              
(-0.250E+00, 0.000E+00)                (-0.266E+00, 0.000E+00)              
( 0.250E+00, 0.000E+00)                ( 0.266E+00, 0.000E+00)              
( 0.250E+00, 0.000E+00)                ( 0.226E+00, 0.000E+00)              
(-0.241E+00, 0.000E+00)                (-0.226E+00, 0.000E+00)              
( 0.241E+00, 0.000E+00)                ( 0.223E+00, 0.000E+00)              
(-0.229E+00, 0.000E+00)                (-0.223E+00, 0.000E+00)              
( 0.229E+00, 0.000E+00)                (-0.208E+00, 0.000E+00)              
(-0.226E+00, 0.000E+00)                ( 0.208E+00, 0.000E+00)              
( 0.226E+00, 0.000E+00)                ( 0.197E+00, 0.000E+00)              
( 0.207E+00, 0.000E+00)                (-0.197E+00, 0.000E+00)              
(-0.207E+00, 0.000E+00)                ( 0.186E+00, 0.000E+00)              
( 0.206E+00, 0.000E+00)                (-0.186E+00, 0.000E+00)              
( 0.176E+00, 0.000E+00)                ( 0.173E+00, 0.000E+00)              
(-0.176E+00, 0.000E+00)                (-0.173E+00, 0.000E+00)              
(-0.155E+00, 0.000E+00)                ( 0.148E+00, 0.000E+00)              
( 0.155E+00, 0.000E+00)                (-0.148E+00, 0.000E+00)              
( 0.117E+00, 0.000E+00)                ( 0.127E+00, 0.000E+00)              
( 0.955E-01, 0.000E+00)                (-0.127E+00, 0.000E+00)              
( 0.955E-01, 0.000E+00)                (-0.862E-01, 0.000E+00)              
(-0.955E-01, 0.000E+00)                ( 0.862E-01, 0.000E+00)              
(-0.925E-01, 0.000E+00)                (-0.834E-01, 0.000E+00)              
( 0.925E-01, 0.000E+00)                ( 0.834E-01, 0.000E+00)              
(-0.891E-01, 0.000E+00)                (-0.771E-01, 0.000E+00)              
( 0.891E-01, 0.000E+00)                ( 0.771E-01, 0.000E+00)              
(-0.868E-01, 0.000E+00)                (-0.752E-01, 0.000E+00)              
( 0.868E-01, 0.000E+00)                ( 0.752E-01, 0.000E+00)              
( 0.677E-01, 0.000E+00)                (-0.712E-01, 0.000E+00)              
(-0.677E-01, 0.000E+00)                ( 0.712E-01, 0.000E+00)              
(-0.653E-01, 0.000E+00)                ( 0.549E-01, 0.000E+00)              
( 0.653E-01, 0.000E+00)                (-0.549E-01, 0.000E+00)              
( 0.439E-01, 0.000E+00)                (-0.532E-01, 0.000E+00)              
(-0.439E-01, 0.000E+00)                ( 0.532E-01, 0.000E+00)              
( 0.302E-01, 0.000E+00)                ( 0.335E-01, 0.000E+00)              
( 0.245E-01, 0.000E+00)                (-0.335E-01, 0.000E+00)              
( 0.215E-01, 0.000E+00)                ( 0.161E-01, 0.000E+00)              
(-0.215E-01, 0.000E+00)                (-0.161E-01, 0.000E+00)              
(-0.568E-02, 0.000E+00)                ( 0.422E-02, 0.000E+00)              
( 0.568E-02, 0.000E+00)                (-0.422E-02, 0.000E+00)              
( 0.251E-14, 0.857E-15)
( 0.251E-14,-0.857E-15)
(-0.255E-14, 0.000E+00)
( 0.233E-15, 0.235E-14)
( 0.233E-15,-0.235E-14)
(-0.124E-14, 0.565E-15)
(-0.124E-14,-0.565E-15)
( 0.113E-14, 0.000E+00)
(-0.772E-15, 0.000E+00)
( 0.632E-15, 0.207E-15)
( 0.632E-15,-0.207E-15)
(-0.490E-15, 0.439E-15)
(-0.490E-15,-0.439E-15)
( 0.165E-15, 0.488E-15)
( 0.165E-15,-0.488E-15)
( 0.458E-15, 0.000E+00)
(-0.433E-15, 0.000E+00)
(-0.330E-15, 0.101E-15)
(-0.330E-15,-0.101E-15)
( 0.212E-15, 0.141E-15)
( 0.212E-15,-0.141E-15)
(-0.123E-15, 0.217E-15)
(-0.123E-15,-0.217E-15)
( 0.750E-17, 0.128E-15)
( 0.750E-17,-0.128E-15)
( 0.277E-16, 0.412E-16)
( 0.277E-16,-0.412E-16)
(-0.217E-16, 0.252E-16)
(-0.217E-16,-0.252E-16)
( 0.327E-16, 0.000E+00)
(-0.230E-16, 0.000E+00)
(-0.824E-30, 0.885E-30)
(-0.824E-30,-0.885E-30)
( 0.680E-30, 0.000E+00)
(-0.684E-31, 0.000E+00)
( 0.317E-31, 0.000E+00)
( 0.000E+00, 0.000E+00)
( 0.000E+00, 0.000E+00)
( 0.000E+00, 0.000E+00)
( 0.000E+00, 0.000E+00)
( 0.000E+00, 0.000E+00)
( 0.000E+00, 0.000E+00)

Condição de Neumann em todos os lados e subtraindo P(1,2)

Usando 

 Pnew=Pnew -P(1,2)

temos o espectro abaixo. 

 Incluindo CC na Matriz                 Excluindo CC na Matriz
lambda(1)=  0.975528258147575          lambda(1)=  0.955274744954828
lambda(n)=  0.000000000000000E+000     lambda(n)=  0.000000000000000E+000

( 0.976E+00, 0.0      )     (-0.955E+00, 0.0      )
( 0.970E+00, 0.0      )     ( 0.911E+00, 0.0      )
( 0.945E+00, 0.0      )     ( 0.896E+00, 0.0      )
(-0.945E+00, 0.0      )     (-0.896E+00, 0.0      )
( 0.905E+00, 0.0      )     ( 0.884E+00, 0.0      )
( 0.883E+00, 0.0      )     (-0.884E+00, 0.0      )
(-0.874E+00, 0.0      )     (-0.825E+00, 0.0      )
( 0.874E+00, 0.0      )     ( 0.825E+00, 0.0      )
( 0.859E+00, 0.0      )     (-0.803E+00, 0.0      )
(-0.859E+00, 0.0      )     ( 0.789E+00, 0.0      )
( 0.794E+00, 0.0      )     (-0.774E+00, 0.0      )
( 0.788E+00, 0.0      )     (-0.732E+00, 0.0      )
(-0.788E+00, 0.0      )     ( 0.732E+00, 0.0      )
( 0.764E+00, 0.0      )     ( 0.715E+00, 0.0      )
(-0.764E+00, 0.0      )     (-0.712E+00, 0.0      )
( 0.750E+00, 0.0      )     ( 0.693E+00, 0.0      )
(-0.726E+00, 0.0      )     ( 0.683E+00, 0.0      )
( 0.726E+00, 0.0      )     (-0.682E+00, 0.0      )
(-0.677E+00, 0.0      )     (-0.634E+00, 0.0      )
( 0.677E+00, 0.0      )     ( 0.634E+00, 0.0      )
( 0.655E+00, 0.0      )     (-0.621E+00, 0.0      )
(-0.655E+00, 0.0      )     (-0.612E+00, 0.0      )
( 0.655E+00, 0.0      )     ( 0.612E+00, 0.0      )
(-0.624E+00, 0.0      )     ( 0.583E+00, 0.0      )
( 0.624E+00, 0.0      )     (-0.575E+00, 0.0      )
( 0.587E+00, 0.0      )     ( 0.575E+00, 0.0      )
( 0.562E+00, 0.0      )     (-0.547E+00, 0.0      )
(-0.562E+00, 0.0      )     ( 0.507E+00, 0.0      )
( 0.544E+00, 0.0      )     ( 0.502E+00, 0.0      )
(-0.544E+00, 0.0      )     (-0.494E+00, 0.0      )
(-0.538E+00, 0.0      )     ( 0.482E+00, 0.0      )
( 0.538E+00, 0.0      )     (-0.482E+00, 0.0      )
( 0.500E+00, 0.0      )     (-0.480E+00, 0.0      )
( 0.491E+00, 0.0      )     (-0.476E+00, 0.0      )
(-0.491E+00, 0.0      )     ( 0.476E+00, 0.0      )
(-0.470E+00, 0.0      )     ( 0.421E+00, 0.0      )
( 0.470E+00, 0.0      )     (-0.416E+00, 0.0      )
( 0.413E+00, 0.0      )     ( 0.412E+00, 0.0      )
(-0.405E+00, 0.0      )     ( 0.404E+00, 0.0      )
( 0.405E+00, 0.0      )     (-0.402E+00, 0.0      )
(-0.389E+00, 0.0      )     (-0.365E+00, 0.0      )
( 0.389E+00, 0.0      )     (-0.362E+00, 0.0      )
( 0.383E+00, 0.0      )     ( 0.362E+00, 0.0      )
(-0.383E+00, 0.0      )     ( 0.343E+00, 0.0      )
(-0.381E+00, 0.0      )     ( 0.333E+00, 0.0      )
( 0.381E+00, 0.0      )     (-0.333E+00, 0.0      )
( 0.345E+00, 0.0      )     (-0.327E+00, 0.0      )
( 0.318E+00, 0.0      )     (-0.325E+00, 0.0      )
(-0.318E+00, 0.0      )     ( 0.325E+00, 0.0      )
( 0.315E+00, 0.0      )     ( 0.283E+00, 0.0      )
(-0.315E+00, 0.0      )     (-0.268E+00, 0.0      )
( 0.250E+00, 0.0      )     ( 0.266E+00, 0.0      )
(-0.250E+00, 0.0      )     (-0.266E+00, 0.0      )
( 0.250E+00, 0.0      )     (-0.226E+00, 0.0      )
( 0.241E+00, 0.0      )     ( 0.226E+00, 0.0      )
(-0.241E+00, 0.0      )     ( 0.223E+00, 0.0      )
(-0.229E+00, 0.0      )     (-0.218E+00, 0.0      )
( 0.229E+00, 0.0      )     ( 0.208E+00, 0.0      )
(-0.226E+00, 0.0      )     ( 0.202E+00, 0.0      )
( 0.226E+00, 0.0      )     (-0.197E+00, 0.0      )
( 0.207E+00, 0.0      )     ( 0.197E+00, 0.0      )
(-0.207E+00, 0.0      )     (-0.190E+00, 0.0      )
( 0.206E+00, 0.0      )     (-0.186E+00, 0.0      )
( 0.176E+00, 0.0      )     (-0.173E+00, 0.0      )
(-0.176E+00, 0.0      )     ( 0.173E+00, 0.0      )
( 0.155E+00, 0.0      )     ( 0.148E+00, 0.0      )
(-0.155E+00, 0.0      )     (-0.146E+00, 0.0      )
( 0.117E+00, 0.0      )     ( 0.127E+00, 0.0      )
(-0.955E-01, 0.0      )     ( 0.122E+00, 0.0      )
( 0.955E-01, 0.411E-15)     (-0.120E+00, 0.0      )
( 0.955E-01,-0.411E-15)     (-0.862E-01, 0.0      )
( 0.925E-01, 0.0      )     (-0.834E-01, 0.0      )
(-0.925E-01, 0.0      )     ( 0.834E-01, 0.0      )
(-0.891E-01, 0.0      )     ( 0.789E-01, 0.0      )
( 0.891E-01, 0.0      )     (-0.771E-01, 0.0      )
( 0.868E-01, 0.0      )     ( 0.771E-01, 0.0      )
(-0.868E-01, 0.0      )     (-0.752E-01, 0.0      )
(-0.677E-01, 0.0      )     ( 0.752E-01, 0.0      )
( 0.677E-01, 0.0      )     (-0.712E-01, 0.0      )
( 0.653E-01, 0.0      )     ( 0.573E-01, 0.0      )
(-0.653E-01, 0.0      )     (-0.549E-01, 0.0      )
(-0.439E-01, 0.0      )     (-0.532E-01, 0.0      )
( 0.439E-01, 0.0      )     ( 0.532E-01, 0.0      )
( 0.302E-01, 0.0      )     ( 0.395E-01, 0.0      )
( 0.245E-01, 0.0      )     (-0.335E-01, 0.0      )
(-0.215E-01, 0.0      )     (-0.161E-01, 0.0      )
( 0.215E-01, 0.0      )     ( 0.161E-01, 0.0      )
( 0.568E-02, 0.0      )     ( 0.523E-02, 0.0      )
(-0.568E-02, 0.0      )     (-0.422E-02, 0.0      )
(-0.444E-14, 0.0      )     ( 0.0      , 0.0      )
( 0.214E-14, 0.128E-14)
( 0.214E-14,-0.128E-14)
( 0.217E-14, 0.0      )
(-0.168E-14, 0.0      )
(-0.140E-14, 0.798E-15)
(-0.140E-14,-0.798E-15)
(-0.890E-15, 0.126E-14)
(-0.890E-15,-0.126E-14)
( 0.565E-15, 0.105E-14)
( 0.565E-15,-0.105E-14)
( 0.876E-15, 0.0      )
(-0.773E-15, 0.208E-15)
(-0.773E-15,-0.208E-15)
( 0.587E-15, 0.0      )
(-0.150E-16, 0.567E-15)
(-0.150E-16,-0.567E-15)
( 0.352E-15, 0.337E-15)
( 0.352E-15,-0.337E-15)
( 0.127E-15, 0.324E-15)
( 0.127E-15,-0.324E-15)
(-0.137E-16, 0.199E-15)
(-0.137E-16,-0.199E-15)
( 0.172E-15, 0.372E-16)
( 0.172E-15,-0.372E-16)
( 0.719E-16, 0.157E-15)
( 0.719E-16,-0.157E-15)
(-0.153E-15, 0.661E-16)
(-0.153E-15,-0.661E-16)
(-0.304E-16, 0.683E-16)
(-0.304E-16,-0.683E-16)
(-0.192E-16, 0.0      )
(-0.955E-28, 0.0      )
(-0.281E-30, 0.325E-30)
(-0.281E-30,-0.325E-30)
( 0.0      , 0.0      )
( 0.0      , 0.0      )
( 0.0      , 0.0      )
( 0.0      , 0.0      )
( 0.0      , 0.0      )
( 0.0      , 0.0      )
( 0.0      , 0.0      )
( 0.0      , 0.0      )

Condição de Neumann em todos os lados fixando um ponto, P(1,2)=1

Usando CC de Neumann e fixando em um ponto 

 Pnew(1,2)=P(1,2)

Temos o espectro abaixo. 

 lambda(1)=   1.00000000000000         lambda(1)=  0.955274744954830
 lambda(n)=  0.000000000000000E+000    lambda(n)=  4.218228659674831E-003  
      Eigenvalues                           Eigenvalues                    
( 0.100E+01, 0.000E+00)               (-0.955E+00, 0.000E+00)              
( 0.999E+00, 0.000E+00)               ( 0.955E+00, 0.000E+00)              
( 0.974E+00, 0.000E+00)               (-0.896E+00, 0.000E+00)              
( 0.967E+00, 0.000E+00)               ( 0.896E+00, 0.000E+00)              
(-0.945E+00, 0.000E+00)               ( 0.884E+00, 0.000E+00)              
( 0.939E+00, 0.000E+00)               (-0.884E+00, 0.000E+00)              
( 0.902E+00, 0.000E+00)               ( 0.825E+00, 0.000E+00)              
( 0.881E+00, 0.000E+00)               (-0.825E+00, 0.000E+00)              
(-0.874E+00, 0.000E+00)               (-0.803E+00, 0.000E+00)              
( 0.869E+00, 0.000E+00)               ( 0.803E+00, 0.000E+00)              
(-0.859E+00, 0.000E+00)               ( 0.774E+00, 0.000E+00)              
( 0.849E+00, 0.000E+00)               (-0.774E+00, 0.000E+00)              
( 0.793E+00, 0.000E+00)               ( 0.732E+00, 0.000E+00)              
(-0.788E+00, 0.000E+00)               (-0.732E+00, 0.000E+00)              
( 0.782E+00, 0.000E+00)               ( 0.715E+00, 0.000E+00)              
(-0.764E+00, 0.000E+00)               (-0.715E+00, 0.000E+00)              
( 0.758E+00, 0.000E+00)               ( 0.683E+00, 0.000E+00)              
( 0.746E+00, 0.000E+00)               (-0.683E+00, 0.000E+00)              
(-0.726E+00, 0.000E+00)               (-0.634E+00, 0.000E+00)              
( 0.718E+00, 0.000E+00)               ( 0.634E+00, 0.000E+00)              
(-0.677E+00, 0.000E+00)               ( 0.621E+00, 0.000E+00)              
( 0.672E+00, 0.000E+00)               (-0.621E+00, 0.000E+00)              
(-0.655E+00, 0.000E+00)               ( 0.612E+00, 0.000E+00)              
( 0.655E+00, 0.000E+00)               (-0.612E+00, 0.000E+00)              
( 0.645E+00, 0.000E+00)               ( 0.575E+00, 0.000E+00)              
(-0.625E+00, 0.000E+00)               (-0.575E+00, 0.000E+00)              
( 0.617E+00, 0.000E+00)               ( 0.547E+00, 0.000E+00)              
( 0.584E+00, 0.000E+00)               (-0.547E+00, 0.000E+00)              
(-0.563E+00, 0.000E+00)               ( 0.502E+00, 0.000E+00)              
( 0.558E+00, 0.000E+00)               (-0.502E+00, 0.000E+00)              
(-0.545E+00, 0.000E+00)               ( 0.482E+00, 0.000E+00)              
( 0.541E+00, 0.000E+00)               (-0.482E+00, 0.000E+00)              
(-0.538E+00, 0.000E+00)               ( 0.480E+00, 0.000E+00)              
( 0.527E+00, 0.000E+00)               (-0.480E+00, 0.000E+00)              
( 0.498E+00, 0.000E+00)               ( 0.476E+00, 0.000E+00)              
(-0.492E+00, 0.000E+00)               (-0.476E+00, 0.000E+00)              
( 0.485E+00, 0.000E+00)               ( 0.421E+00, 0.000E+00)              
(-0.470E+00, 0.000E+00)               (-0.421E+00, 0.000E+00)              
( 0.462E+00, 0.000E+00)               ( 0.404E+00, 0.000E+00)              
( 0.412E+00, 0.000E+00)               (-0.404E+00, 0.000E+00)              
(-0.406E+00, 0.000E+00)               ( 0.365E+00, 0.000E+00)              
( 0.401E+00, 0.000E+00)               (-0.365E+00, 0.000E+00)              
(-0.389E+00, 0.000E+00)               ( 0.362E+00, 0.000E+00)              
( 0.387E+00, 0.000E+00)               (-0.362E+00, 0.000E+00)              
(-0.384E+00, 0.000E+00)               (-0.333E+00, 0.000E+00)              
( 0.382E+00, 0.000E+00)               ( 0.333E+00, 0.000E+00)              
(-0.382E+00, 0.000E+00)               ( 0.327E+00, 0.000E+00)              
( 0.366E+00, 0.000E+00)               (-0.327E+00, 0.000E+00)              
( 0.343E+00, 0.000E+00)               (-0.325E+00, 0.000E+00)              
(-0.319E+00, 0.000E+00)               ( 0.325E+00, 0.000E+00)              
( 0.317E+00, 0.000E+00)               (-0.268E+00, 0.000E+00)              
(-0.316E+00, 0.000E+00)               ( 0.268E+00, 0.000E+00)              
( 0.306E+00, 0.000E+00)               (-0.266E+00, 0.000E+00)              
(-0.253E+00, 0.000E+00)               ( 0.266E+00, 0.000E+00)              
( 0.250E+00, 0.000E+00)               ( 0.226E+00, 0.000E+00)              
( 0.247E+00, 0.000E+00)               (-0.226E+00, 0.000E+00)              
(-0.243E+00, 0.000E+00)               ( 0.223E+00, 0.000E+00)              
( 0.237E+00, 0.000E+00)               (-0.223E+00, 0.000E+00)              
(-0.230E+00, 0.000E+00)               (-0.208E+00, 0.000E+00)              
( 0.227E+00, 0.000E+00)               ( 0.208E+00, 0.000E+00)              
(-0.226E+00, 0.000E+00)               ( 0.197E+00, 0.000E+00)              
( 0.219E+00, 0.000E+00)               (-0.197E+00, 0.000E+00)              
(-0.209E+00, 0.000E+00)               ( 0.186E+00, 0.000E+00)              
( 0.206E+00, 0.000E+00)               (-0.186E+00, 0.000E+00)              
( 0.197E+00, 0.000E+00)               ( 0.173E+00, 0.000E+00)              
(-0.176E+00, 0.000E+00)               (-0.173E+00, 0.000E+00)              
( 0.172E+00, 0.000E+00)               ( 0.148E+00, 0.000E+00)              
(-0.156E+00, 0.000E+00)               (-0.148E+00, 0.000E+00)              
( 0.150E+00, 0.000E+00)               ( 0.127E+00, 0.000E+00)              
( 0.116E+00, 0.000E+00)               (-0.127E+00, 0.000E+00)              
(-0.102E+00, 0.000E+00)               (-0.862E-01, 0.000E+00)              
( 0.955E-01, 0.000E+00)               ( 0.862E-01, 0.000E+00)              
( 0.941E-01, 0.000E+00)               (-0.834E-01, 0.000E+00)              
(-0.930E-01, 0.000E+00)               ( 0.834E-01, 0.000E+00)              
( 0.916E-01, 0.000E+00)               (-0.771E-01, 0.000E+00)              
(-0.911E-01, 0.000E+00)               ( 0.771E-01, 0.000E+00)              
( 0.882E-01, 0.000E+00)               (-0.752E-01, 0.000E+00)              
(-0.881E-01, 0.000E+00)               ( 0.752E-01, 0.000E+00)              
( 0.795E-01, 0.000E+00)               (-0.712E-01, 0.000E+00)              
(-0.708E-01, 0.000E+00)               ( 0.712E-01, 0.000E+00)              
( 0.660E-01, 0.000E+00)               ( 0.549E-01, 0.000E+00)              
(-0.655E-01, 0.000E+00)               (-0.549E-01, 0.000E+00)              
( 0.587E-01, 0.000E+00)               (-0.532E-01, 0.000E+00)              
(-0.463E-01, 0.000E+00)               ( 0.532E-01, 0.000E+00)              
( 0.389E-01, 0.000E+00)               ( 0.335E-01, 0.000E+00)              
( 0.298E-01, 0.000E+00)               (-0.335E-01, 0.000E+00)              
( 0.243E-01, 0.000E+00)               ( 0.161E-01, 0.000E+00)              
(-0.229E-01, 0.000E+00)               (-0.161E-01, 0.000E+00)              
( 0.186E-01, 0.000E+00)               ( 0.422E-02, 0.000E+00)              
(-0.615E-02, 0.000E+00)               (-0.422E-02, 0.000E+00)              
( 0.500E-02, 0.000E+00)                                                    
(-0.799E-14, 0.000E+00)
( 0.595E-14, 0.000E+00)
(-0.228E-14, 0.000E+00)
(-0.173E-14, 0.900E-15)
(-0.173E-14,-0.900E-15)
( 0.176E-14, 0.000E+00)
( 0.906E-15, 0.488E-15)
( 0.906E-15,-0.488E-15)
(-0.669E-15, 0.726E-15)
(-0.669E-15,-0.726E-15)
( 0.756E-15, 0.000E+00)
(-0.694E-15, 0.000E+00)
(-0.592E-16, 0.509E-15)
(-0.592E-16,-0.509E-15)
( 0.451E-15, 0.209E-15)
( 0.451E-15,-0.209E-15)
( 0.995E-16, 0.355E-15)
( 0.995E-16,-0.355E-15)
(-0.226E-15, 0.206E-15)
(-0.226E-15,-0.206E-15)
(-0.240E-15, 0.000E+00)
( 0.157E-15, 0.000E+00)
( 0.110E-16, 0.108E-15)
( 0.110E-16,-0.108E-15)
(-0.407E-16, 0.954E-16)
(-0.407E-16,-0.954E-16)
( 0.798E-16, 0.494E-16)
( 0.798E-16,-0.494E-16)
(-0.372E-16, 0.000E+00)
( 0.172E-17, 0.943E-17)
( 0.172E-17,-0.943E-17)
( 0.454E-26, 0.000E+00)
(-0.800E-30, 0.213E-30)
(-0.800E-30,-0.213E-30)
( 0.683E-30, 0.000E+00)
(-0.556E-31, 0.000E+00)
( 0.000E+00, 0.000E+00)
( 0.000E+00, 0.000E+00)
( 0.000E+00, 0.000E+00)
( 0.000E+00, 0.000E+00)
( 0.000E+00, 0.000E+00)

Condição de Neumann em 3 lados fixando P=1 na entrada (ou na saída)

O espectro tem a maioria dos autovalores próximos do eixo real com alguns autovalores complexos (um pequeno circulo de valores complexos dentro do círculo unitário) com σ ⊂ 11.26 ∪ (-1,1) incluindo 0. 

 lambda(1)=   1.00000000000000         lambda(1)=  0.955274744954830
 lambda(n)=  0.000000000000000E+000    lambda(n)=  4.218228659674831E-003  
      Eigenvalues                           Eigenvalues                    
( 0.100E+01, 0.000E+00)              
( 0.100E+01, 0.000E+00)              
( 0.100E+01, 0.000E+00)              
( 0.100E+01, 0.000E+00)              
( 0.100E+01, 0.000E+00)              
( 0.100E+01, 0.000E+00)              
( 0.100E+01, 0.000E+00)              
( 0.100E+01, 0.000E+00)              
( 0.100E+01, 0.000E+00)              
( 0.100E+01, 0.000E+00)              
( 0.100E+01, 0.000E+00)              
( 0.994E+00, 0.000E+00)               (-0.955E+00, 0.000E+00)
( 0.964E+00, 0.000E+00)               ( 0.955E+00, 0.000E+00)              
( 0.950E+00, 0.000E+00)               (-0.896E+00, 0.000E+00)              
(-0.948E+00, 0.000E+00)               ( 0.896E+00, 0.000E+00)              
( 0.920E+00, 0.000E+00)               ( 0.884E+00, 0.000E+00)              
(-0.883E+00, 0.000E+00)               (-0.884E+00, 0.000E+00)              
( 0.877E+00, 0.000E+00)               ( 0.825E+00, 0.000E+00)              
( 0.867E+00, 0.000E+00)               (-0.825E+00, 0.000E+00)              
(-0.861E+00, 0.000E+00)               (-0.803E+00, 0.000E+00)              
( 0.836E+00, 0.000E+00)               ( 0.803E+00, 0.000E+00)              
( 0.834E+00, 0.000E+00)               ( 0.774E+00, 0.000E+00)              
(-0.796E+00, 0.000E+00)               (-0.774E+00, 0.000E+00)              
(-0.782E+00, 0.000E+00)               ( 0.732E+00, 0.000E+00)              
( 0.750E+00, 0.000E+00)               (-0.732E+00, 0.000E+00)              
( 0.750E+00, 0.000E+00)               ( 0.715E+00, 0.000E+00)              
( 0.744E+00, 0.000E+00)               (-0.715E+00, 0.000E+00)              
(-0.728E+00, 0.000E+00)               ( 0.683E+00, 0.000E+00)              
( 0.720E+00, 0.000E+00)               (-0.683E+00, 0.000E+00)              
( 0.700E+00, 0.000E+00)               (-0.634E+00, 0.000E+00)              
(-0.695E+00, 0.000E+00)               ( 0.634E+00, 0.000E+00)              
(-0.663E+00, 0.000E+00)               ( 0.621E+00, 0.000E+00)              
(-0.653E+00, 0.000E+00)               (-0.621E+00, 0.000E+00)              
( 0.633E+00, 0.000E+00)               ( 0.612E+00, 0.000E+00)              
( 0.617E+00, 0.000E+00)               (-0.612E+00, 0.000E+00)              
( 0.611E+00, 0.000E+00)               ( 0.575E+00, 0.000E+00)              
( 0.581E+00, 0.000E+00)               (-0.575E+00, 0.000E+00)              
( 0.581E+00, 0.000E+00)               ( 0.547E+00, 0.000E+00)              
(-0.566E+00, 0.000E+00)               (-0.547E+00, 0.000E+00)              
(-0.565E+00, 0.000E+00)               ( 0.502E+00, 0.000E+00)              
(-0.562E+00, 0.000E+00)               (-0.502E+00, 0.000E+00)              
( 0.537E+00, 0.000E+00)               ( 0.482E+00, 0.000E+00)              
(-0.507E+00, 0.000E+00)               (-0.482E+00, 0.000E+00)              
( 0.500E+00, 0.000E+00)               ( 0.480E+00, 0.000E+00)              
(-0.500E+00, 0.000E+00)               (-0.480E+00, 0.000E+00)              
( 0.494E+00, 0.000E+00)               ( 0.476E+00, 0.000E+00)              
( 0.463E+00, 0.000E+00)               (-0.476E+00, 0.000E+00)              
( 0.453E+00, 0.000E+00)               ( 0.421E+00, 0.000E+00)              
(-0.433E+00, 0.000E+00)               (-0.421E+00, 0.000E+00)              
( 0.432E+00, 0.000E+00)               ( 0.404E+00, 0.000E+00)              
(-0.420E+00, 0.000E+00)               (-0.404E+00, 0.000E+00)              
( 0.408E+00, 0.000E+00)               ( 0.365E+00, 0.000E+00)              
(-0.399E+00, 0.000E+00)               (-0.365E+00, 0.000E+00)              
(-0.391E+00, 0.000E+00)               ( 0.362E+00, 0.000E+00)              
( 0.364E+00, 0.000E+00)               (-0.362E+00, 0.000E+00)              
( 0.361E+00, 0.000E+00)               (-0.333E+00, 0.000E+00)              
(-0.359E+00, 0.000E+00)               ( 0.333E+00, 0.000E+00)              
( 0.346E+00, 0.000E+00)               ( 0.327E+00, 0.000E+00)              
( 0.337E+00, 0.000E+00)               (-0.327E+00, 0.000E+00)              
(-0.326E+00, 0.000E+00)               (-0.325E+00, 0.000E+00)              
( 0.317E+00, 0.000E+00)               ( 0.325E+00, 0.000E+00)              
(-0.287E+00, 0.000E+00)               (-0.268E+00, 0.000E+00)              
( 0.287E+00, 0.000E+00)               ( 0.268E+00, 0.000E+00)              
( 0.280E+00, 0.000E+00)               (-0.266E+00, 0.000E+00)              
(-0.272E+00, 0.000E+00)               ( 0.266E+00, 0.000E+00)              
(-0.269E+00, 0.000E+00)               ( 0.226E+00, 0.000E+00)              
( 0.244E+00, 0.000E+00)               (-0.226E+00, 0.000E+00)              
(-0.228E+00, 0.000E+00)               ( 0.223E+00, 0.000E+00)              
(-0.225E+00, 0.000E+00)               (-0.223E+00, 0.000E+00)              
(-0.220E+00, 0.000E+00)               (-0.208E+00, 0.000E+00)              
( 0.213E+00, 0.000E+00)               ( 0.208E+00, 0.000E+00)              
( 0.200E+00, 0.000E+00)               ( 0.197E+00, 0.000E+00)              
( 0.200E+00, 0.000E+00)               (-0.197E+00, 0.000E+00)              
( 0.198E+00, 0.000E+00)               ( 0.186E+00, 0.000E+00)              
( 0.188E+00, 0.000E+00)               (-0.186E+00, 0.000E+00)              
( 0.163E+00, 0.000E+00)               ( 0.173E+00, 0.000E+00)              
(-0.163E+00, 0.000E+00)               (-0.173E+00, 0.000E+00)              
( 0.158E+00, 0.000E+00)               ( 0.148E+00, 0.000E+00)              
(-0.139E+00, 0.000E+00)               (-0.148E+00, 0.000E+00)              
(-0.133E+00, 0.000E+00)               ( 0.127E+00, 0.000E+00)              
(-0.124E+00, 0.000E+00)               (-0.127E+00, 0.000E+00)              
( 0.117E+00, 0.000E+00)               (-0.862E-01, 0.000E+00)              
( 0.111E+00, 0.000E+00)               ( 0.862E-01, 0.000E+00)              
(-0.103E+00, 0.000E+00)               (-0.834E-01, 0.000E+00)              
(-0.958E-01, 0.000E+00)               ( 0.834E-01, 0.000E+00)              
(-0.948E-01, 0.000E+00)               (-0.771E-01, 0.000E+00)              
( 0.869E-01, 0.000E+00)               ( 0.771E-01, 0.000E+00)              
( 0.713E-01, 0.000E+00)               (-0.752E-01, 0.000E+00)              
( 0.675E-01, 0.000E+00)               ( 0.752E-01, 0.000E+00)              
( 0.673E-01, 0.000E+00)               (-0.712E-01, 0.000E+00)              
(-0.617E-01, 0.000E+00)               ( 0.712E-01, 0.000E+00)              
( 0.567E-01, 0.000E+00)               ( 0.549E-01, 0.000E+00)              
( 0.495E-01, 0.000E+00)               (-0.549E-01, 0.000E+00)              
(-0.301E-01, 0.000E+00)               (-0.532E-01, 0.000E+00)              
( 0.246E-01, 0.000E+00)               ( 0.532E-01, 0.000E+00)              
( 0.244E-01, 0.000E+00)               ( 0.335E-01, 0.000E+00)              
( 0.222E-01, 0.000E+00)               (-0.335E-01, 0.000E+00)              
(-0.194E-01, 0.000E+00)               ( 0.161E-01, 0.000E+00)              
(-0.165E-01, 0.000E+00)               (-0.161E-01, 0.000E+00)              
(-0.794E-02, 0.000E+00)               ( 0.422E-02, 0.000E+00)              
( 0.841E-09, 0.000E+00)               (-0.422E-02, 0.000E+00)              
(-0.841E-09, 0.000E+00)
(-0.308E-13, 0.000E+00)
( 0.297E-14, 0.401E-15)
( 0.297E-14,-0.401E-15)
(-0.245E-14, 0.000E+00)
( 0.124E-14, 0.000E+00)
(-0.702E-15, 0.693E-15)
(-0.702E-15,-0.693E-15)
( 0.671E-15, 0.438E-15)
( 0.671E-15,-0.438E-15)
(-0.404E-15, 0.517E-15)
(-0.404E-15,-0.517E-15)
( 0.230E-15, 0.290E-15)
( 0.230E-15,-0.290E-15)
(-0.317E-15, 0.000E+00)
(-0.302E-15, 0.000E+00)
(-0.589E-16, 0.240E-15)
(-0.589E-16,-0.240E-15)
(-0.138E-15, 0.790E-16)
(-0.138E-15,-0.790E-16)
( 0.146E-15, 0.000E+00)
(-0.599E-16, 0.168E-16)
(-0.599E-16,-0.168E-16)
( 0.309E-16, 0.000E+00)
( 0.123E-16, 0.000E+00)
(-0.442E-17, 0.108E-16)
(-0.442E-17,-0.108E-16)
(-0.940E-30, 0.000E+00)
( 0.000E+00, 0.000E+00)
( 0.000E+00, 0.000E+00)
( 0.000E+00, 0.000E+00)

Teste 5

Disponível em "http://hunter.mat.ufrgs.br/mediawiki/index.php?title=Análise_espectral_e_estabilidade&oldid=1678"