Integration time step for coupled ODEs
I am using the implicit Euler method to solve a coupled system of ODEs (temperature + chemical species) with convection, diffusion and (stiff) reactions. The number of species is about 30 and the number of points is about 100,000, which means that the total number of equations is quite large (3,000,000). I am using MUMPS to solve the corresponding linear systems.
I am looking to a smart methodology to choose and modify the integration time step size during the calculations, in order to minimize the total number of steps to reach the final solution (which corresponds to the steady state conditions). In the current version of my code I increase the time step with a fixed ratio, but I think this approach is not so efficient. I was wondering if a better technique is available.
Thanks a lot.
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