## Solve parabolic coupled PDE's using MATLAB's pdepe solver?

### Jacob (view profile)

on 5 Jun 2014
Latest activity Commented on by asim asrar

### asim asrar (view profile)

on 9 Jul 2018
Accepted Answer by Bill Greene

### Bill Greene (view profile)

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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

### Bill Greene (view profile)

Answer by Bill Greene

### Bill Greene (view profile)

on 5 Jun 2014

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

Jacob

### Jacob (view profile)

on 5 Jun 2014
Bill, Thanks for the response! I've reviewed the example 2, but still have a question. I know this may be basic for you and I really appreciate your help!
In example 2,
f = [0.024; 0.17] .* DuDx
If I'm understanding correctly, DuDx refers to Du1dx for the first row, and Du2dx for the second row. But in my example, I have pde's include both Du1Dx and Du2Dx in each equation.
Do you know how to incorporate both into the pdepd function? Again, I'm sure this question is basic for you and I greatly appreciate your help ! Thanks

### Jacob (view profile)

on 5 Jun 2014

Bill, Thanks for the response! I've reviewed the example 2, but still have a question. I know this may be basic for you and I really appreciate your help!
In example 2,
f = [0.024; 0.17] .* DuDx
If I'm understanding correctly, DuDx refers to Du1dx for the first row, and Du2dx for the second row. But in my example, I have pde's include both Du1Dx and Du2Dx in each equation.
Do you know how to incorporate both into the pdepd function? Again, I'm sure this question is basic for you and I greatly appreciate your help ! Thanks

Torsten

### Torsten (view profile)

on 25 Apr 2016
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 (view profile)

on 14 Jun 2017
I have a similar question. Can we solve a system of nonlinear parabolic partial differential equations using pde toolbox in matlab?
Ravi Kumar

### Ravi Kumar (view profile)

on 14 Jun 2017
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 (view profile)

Answer by asim asrar

### asim asrar (view profile)

on 9 Jul 2018

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)

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asim asrar

### asim asrar (view profile)

on 9 Jul 2018
so can u please tell me how to solve the system of equations given in the attachment
Torsten

### Torsten (view profile)

on 9 Jul 2018
Use the Method-of-Characteristics or the Method-of-Lines.
Best wishes
Torsten.
asim asrar

### asim asrar (view profile)

on 9 Jul 2018
can u share some similar examples with two variables varying simultaneously using method of lines or method of characteristics.