Help solving this 2d pde
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I'am trying to solve this 2d pde on
note that in the rhs u is evaluated at which we can consider as a deviation
where . I used a uniform discretization and got:
As an example we can take and BC
I don't see how to generate the system of equations and corresponding matrix.
Any help or other method to investigate is appreciated.
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Bjorn Gustavsson
on 10 Mar 2020
You are in luck! Matlab provides you with a (rather hidden) method to give you the 2-D Laplacian in matrix form. Have a look at numgrid.
qwe = delsq(numgrid('S',7));
imagesc(full(qwe))
Also have a look at delsqdemo.
For the nonlinear part you might have to look at the different iterative solvers, pcg, qmr, etc (these tools are outside of my commonly used functions...)
HTH
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