pde1dm with coupled ODEs

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feynman feynman 2024-2-4

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2078051-pde1dm-with-coupled-odes

评论： feynman feynman 2024-2-8

According to the pde1dm manual, pde1dm with coupled ODEs has to do with three additional arguments to the pde1dm function:

[solution,odeSolution] = pde1dm(m,pdeFunc,icFunc,bcFunc,meshPts,timePts,... odeFunc, odeIcFunc,xOde)

However, I just:

pde1dm(m,pdeFunc,icFunc,bcFunc,meshPts,timePts)

as though I were using pdepe and I still got the correct result. Why? So when should one add the three additional arguments to pde1dm?

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Bill Greene 2024-2-6

If you run into problems using pde1dm, I am willing to take a look. But there is no way I can respond based on the scant information you have provided in this post.

In general what I expect is the following:

A complete mathematical description of the problem you are trying to solve including the equations (in math format) and the result you expect to obtain.
A complete listing of your source code, simplified as much as possible, and formatted as a code block so I can easily download and run it.

feynman feynman 2024-2-7

在 MATLAB Online 中打开

To solve ut=uxx through a decomposition into two equations with two unknowns u and ux:

and

function heat
w=1;x=linspace(-pi,pi);t=linspace(0,10);
% sol=pdepe(0,@pde,@ic,@bc,x,t);
sol=pde1dm(0,@pde,@ic,@bc,x,t);
u=sol(:,:,1);surf(x,t,u)
%%
    function [c,f,s]=pde(x,t,u,ux)
        c=[1;0];f=[u(2);u(1)];s=[0;-u(2)];
    end
%%
    function u0=ic(x)
        u0=[cos(x);-sin(x)];
    end
%%
    function [pl,ql,pr,qr]=bc(xl,ul,xr,ur,t)
        pl=[0;ul(2)];ql=[1;0];pr=[0;ur(2)];qr=[1;0];
    end
end

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回答（1 个）

Bill Greene 2024-2-7

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2078051-pde1dm-with-coupled-odes#answer_1404371

Your second equation is an elliptic PDE NOT an ODE because both unknown variables are functions of both x and t.. Accordingly, pdepe(and pde1dm) are able to solve this system.

If you are confused about this issue, you should look more carefully at the definition of an ODE shown as equation 2 in the pde1dm user manual. I looked again at the explanation there and don't have anything to add to that at this point.