您正在关注此问题

您将在关注的内容源中看到更新。
您可能会收到电子邮件，具体取决于您的通信预设项。

How to solve a system of parabolic PDEs and 1st order ODEs?

5 次查看（过去 30 天）

显示更早的评论

Monisha S R 2018-11-13

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes

⋮

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes

评论： Bruno Luong 2018-11-16

I'm trying to solve a system of parabolic ODEs and first-order ODEs. I understand that Matlab's pdepe solver cannot solve 1st-order differential equations. How do I solve this sytem? I also tried solving the DAE system using a mass matrix, but encountered the following error:

Error in ode15s (line 310) [y,yp,f0,dfdy,nFE,nPD,Jfac] = daeic12(odeFcn,odeArgs,t,ICtype,Mt,y,yp0,f0,...

A sample set of equations is given below.

12 个评论
显示 10更早的评论隐藏 10更早的评论

Torsten 2018-11-13

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_636739

⋮

链接

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_636739

As it stands, you can use "pdepe" to solve your system.

For the equations for c3 and c4, you have to prescribe f=0 in the pde function and pl=pr=0, ql=qr=1 in the boundary function of "pdepe".

Monisha S R 2018-11-13

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_636868

⋮

链接

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_636868

Oh thanks Torsten. Let me try. I was of the view that only parabolic and elliptic equations can be solved.

Torsten 2018-11-14

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_637069

⋮

链接

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_637069

编辑：Torsten 2018-11-14

Problematic are 1st order PDEs, but your 0-order PDEs (i..e. ODEs) for c3 and c4 should work.

Bruno Luong 2018-11-14

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_637102

⋮

链接

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_637102

在 MATLAB Online 中打开

I just don't understand your system of equations, doe sthat mean

c1 satisfies eqt (1)
c2 satisfies eqt (1+2)
c3 satisfies eqt (1+3)
c4 satisfies eqt (1+4)

I can't see how the variables (c2-c4) that can meet two partial equations at the same time.

Torsten 2018-11-14

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_637109

⋮

链接

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_637109

As I understand it, c in the first equation is c1. So equation i gives ci.

Bruno Luong 2018-11-14

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_637110

⋮

链接

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_637110

Then the equations are actually independent? This is not a system of PDE strictly speaking but two of them (c1+c2) can be solved with pdede, the other two (c3+c4), be solved with pdepe or ode independently.

Seem odd as question.

Torsten 2018-11-14

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_637114

⋮

链接

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_637114

编辑：Torsten 2018-11-14

We don't know the source terms ...

Monisha S R 2018-11-14

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_637174

⋮

链接

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_637174

@Bruno First equation is for

(edited now). The source terms contain the dependence on other concentrations. For example,

where k is a rate constant and so on.

Bruno Luong 2018-11-14

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_637195

⋮

链接

此评论的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/429546-how-to-solve-a-system-of-parabolic-pdes-and-1st-order-odes#comment_637195

Thanks.

Then PDEPE might work. I still have a little doubt about c3/c4 which is purely time ODE and whereas it wil get into conflict with spatial boundary conditions.

Monisha S R 2018-11-15