USing BVP solver to solve 2-D Laplace’s equation?

I have confusion about how to use the bvp solver to solve the 2-D Laplace’s equation (∇2u=∂2u∂x2+∂2u∂y2=0) with in a boundary (rectangular). Could anyone help or provide any website that can help to impement it ?

Thank you in advance.

[Torsten]

What bvp solver do you mean ?

[Willim]

either bvpc4 or bvpc5

Answer 1

[David Wilson]

If you mean bvp4c, then no it is not suitable since it solves boundary value ODEs in 1D, not PDEs in 2D. To solve Laplace's eqn in 2D, the easiest way is to use a finite difference grid. See https://au.mathworks.com/help/matlab/math/finite-difference-laplacian.html for more details.

[Willim]

Thank you for you answer. I think there is some way. one way is to trun the PDE to ODEs then solve each one seprately. However, I would like to know if there is a way to do it either as 2-d or seprated ODEs

[Torsten]

Approximate the partial derivatives by difference quotients and solve the resulting system of linear equations in the node values using "backslash" or an iterative method:

https://www.mps.mpg.de/phd/numerical-integration-partial-differential-equations-stationary-problems-elliptic-pde