Use pdepe to solve an ode
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I am using the pdepe splver to solve a set of 2 pdes that arou coupled and it works great. However, I now want to couple another equation, which does not have a flux term. Therefore, by the pdepe notation,
m = 0, c = 1, f = 0, and s = u-1 (the s is just an example, not my actual s).
The problem is that pdepe discretization supports only parabolic and elliptic equations, with flux term involving spatial derivative.
How can I couple all three equations if two equations are pdes and one equation is ode.
Torsten on 30 Jun 2022
So your equation is not a PDE, but a simple ODE.
Either you try to artificially set du/dx = 0 at both ends and see whether the results make sense.
Or you use Bill Greene's code who claims that ODEs can be handled therein.
Or - as you wrote that there is another problem with your equations that pdepe cannot handle (sigmoid function) - discretize your equations in space and use ODE15S to solve the resulting system of ordinary differential equations in the grid points. Look up "method-of-lines" for more details.