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Coupled ODE-PDE systems, sovler?

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Robert il 18 Mar 2015
Risposto: Torsten il 18 Mar 2015
Hi everyone,
I'm trying to code a coupled ODE-PDE model using the matlab ODE solvers, im trying to code 3 ODEs of the form
(1) dA/dt= F(B)+ D*(dA/dx)^2
(2) dB/dt= -F(B)+F(C)
(3) dC/dt= -F(C)
where F(B) in equations (1) & (2) are functions of B and F(C) in equations (2) & (3) are functions of C.
where D in equation (1) is a constant and (dA/dx)^2 is a double derivative in the spatial direction.
I can code a script using ode45 that works if I remove my diffusion term but im struggling to code a script including this term? I initially tried to discretize (dA/dx)^2 but then i couldnt find a way to recall A(j+1) A(j) and A(j-1) in the solver thanks

Risposte (1)

Torsten il 18 Mar 2015
There is no ready-to-use solver for a coupled ODE-PDE - system.
You will have to go the way you already tried: discretize the d^2A/dx^2-term in space.
This will give you 3*n ordinary differential equations where n is the number of grid points.
Use ODE15S to solve.
Best wishes


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