Solving Discretized Multivariables System of ODEs

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Meteb Mejbel 2021-7-2

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https://ww2.mathworks.cn/matlabcentral/answers/870873-solving-discretized-multivariables-system-of-odes

评论： Amit Bhowmick 2021-7-5

Hi all,

I am solving PDEs of drift-difussion ion exchange (Nernst Plank equations) as shown in the attached picture (equation (1) and there are two more for B and D species). The dependent variables that I want temporally to solve are the concentration of A, B and D. I have discretized the generic equations using finite volume method for all three species and ended up with long equations ( eq(2) and eq(3) for A and B. As you notice, I have reduced some terms in order to simplify it and make it easier to read. Also, I have not included discretized formula of D since they are all the same). Anyway, I have six boundary conditons (two for each species) and initial conditions at t=0 for all. That is, all rhd terms are known at t=0 when solving for C at t=t+dt.

So my questions are:

1- Which ODE solver should I use? ODE45 and ODE15 solve IVP and bvp4c or bvp5c solve BVPs, but I have both conditions.

2- Each solver that I mentioned in the previous question tend to obtain the solution for just one spatial node, how can I make it work for the whole spatial domain?

3- The discretized ODEs I have are uncoupled since each term in rhs are known from perivous time step. From my poor knowledge, most of ODE solvers accept the coupled ones, so can I still use them? correct me if I am wrong.

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Answer 1

Amit Bhowmick 2021-7-3

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https://ww2.mathworks.cn/matlabcentral/answers/870873-solving-discretized-multivariables-system-of-odes#answer_738938

use pdepe

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Meteb Mejbel 2021-7-5

Hey @Amit Bhowmick I've tried it again and it seems promising except the boundary conditions. I have posted the question to resolve the error I have if you want to look at it.

https://www.mathworks.com/matlabcentral/answers/871848-error-in-my-boundary-conditions-using-pdepe-solver

Amit Bhowmick 2021-7-5