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

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Willim
Willim 2019-4-9
评论： Torsten 2019-4-11
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.

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回答（1 个）

David Wilson
David Wilson 2019-4-10
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.
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Willim
Willim 2019-4-10
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
Torsten 2019-4-11
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

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