1d poisson

[princedudu]

Hi,

I want to ask one question regarding 1d poisson example. It seems that $uj$ is not the true solution. At least the boundary conditions are different. From the numerical results, backward() is not transferring from spectral space to real space. Would you mind explaining this?

Thanks!

[mikaem]

Hi,
I'm assuming that you're referring to the dirichlet_poisson1d.py demo? uj is the solution in real space at the quadrature points. u_hat is the spectral Galerkin solution, that can be evaluated at any point in the domain. If you evaluate at the boundary, you should get the boundary condition (almost exactly)

In [1]: u_hat(-1.0)
Out[1]: array([-2.77555756e-17])

The quadrature points are

In [2]: SD.mesh()
Out[2]: 
array([ 0.99785892,  0.98078528,  0.94693013,  0.89687274,  0.83146961,
    0.75183981,  0.65934582,  0.55557023,  0.44228869,  0.32143947,
    0.19509032,  0.06540313, -0.06540313, -0.19509032, -0.32143947,
   -0.44228869, -0.55557023, -0.65934582, -0.75183981, -0.83146961,
   -0.89687274, -0.94693013, -0.98078528, -0.99785892])