Solve parabolic coupled PDE's using MATLAB's pdepe solver?
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I know that this question may seem simple to some of you, but I'm wondering if MATLAB's pdepe tool can solve a coupled system of parabolic pde's? The general form is:
d(u1)/dt = d2(u1)/x2 - d2(u2)/x2 d(u2)/dt = d2(u2)/x2 - d2(u1)/x2
More specifically, how does the DuDx command work in the pdepe tool? Can I enter an array for the coefficients of the b function and will it know that the second column coefficient corresponds to u2?
Thanks in advance for your time! Jacob
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Bill Greene
2014-6-5
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Yes, pdepe can definitely solve systems of pde. In general, the u argument to the functions you define has as many rows as there are pde in the system.
I'm not sure what you mean by the "b function." Do you mean the bcfun (4th argument to pdepe)? If so, the two arguments, ul and ur have as many rows as there are pde.
Example 2 on the pdepe documentation page here:
shows a two-equation system.
Bill
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Jacob
2014-6-5
0 个投票
6 个评论
Bill Greene
2014-6-5
Possibly you are confused by that funny .* operator.
There are several ways to express what you want in MATLAB. For example, you could define a couple of temporary variables:
Du1Dx = DuDx(1);
Du2Dx = DuDx(2);
f = [3*Du1Dx + 1.23*Du2Dx
4.56*Du1Dx + 8.9*Du2Dx];
(I just made up some arbitrary coefficients.)
Or you could express the same thing more compactly as:
f = [3 1.23; 4.56 8.9]*DuDx;
And, of course, the coefficients could be much more complicated than just simple constants.
Bill
Jacob
2014-6-5
simopera6
2016-4-24
I think I have a similar question Bill. Can you please help me. I have posted a query in the following link in the physicsforums. If you want I can paste it here or you can reply there. Please help me. Thank You
https://www.physicsforums.com/threads/pdepe-solver-for-diffusion-equation-in-a-packed-column.864649/
Torsten
2016-4-25
You have a mixture of partial differential equations and ordinary differential equations. pdepe is not suited to solve such systems. You will have to discretize your PDE equations in space and solve the resulting complete system of ODEs using ODE15S. Look up "Method-of-Lines" for more details.
Best wishes
Torsten.
Aditi
2017-6-14
I have a similar question. Can we solve a system of nonlinear parabolic partial differential equations using pde toolbox in matlab?
Ravi Kumar
2017-6-14
In general, PDE Toolbox supports solution of coupled nonlinear parabolic equations. It is difficult to comment if your specific PDEs can be be solved, without seeing the equations.
asim asrar
2018-7-9
0 个投票
i have a system of coupled wave equations given in attachment , which are varying in time and space simultaneously , can the equations be solved using pdepe command ( equations are given in attachment)
4 个评论
Torsten
2018-7-9
No. "pdepe" is designed to solve parabolic-elliptic PDEs - your second equation is hyperbolic in nature.
Best wishes
Torsten.
asim asrar
2018-7-9
asim asrar
2018-7-9
can u share some similar examples with two variables varying simultaneously using method of lines or method of characteristics.
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