Typically an ODE System which involves 2 different physical problems such as diffusion and advection can be numerically approached by the well known Strang operator splitting scheme. I'm wondering if there's a generalization of this scheme to an arbitrary number of subproblems.
In my case, there's an additional issue: I got 4 subproblems, two of which have a smaller time-scale (Maxwell equations with time-varying medium) than the remaining 2 (advection/diffusion). Any ideas, keywords, hints?
Sure, see in Numerical Recipes "Operator Splitting Methods Generally" and follow the references there...
In general, a problem with different parts can be split, then each part is solved separately, then the solutions for each flow are composed back to obtain the final solution.
For a description of these methods you can refer to A concise introduction to Geometric Numerical Integration by Blanes & Casas and to Geometric Numerical Integration by Hairer, Lubich, Wanner. But, as far as I remember, they do not give example of 3D problems.
As a more specific example, maybe A splitting approach for the magnetic Schrödinger equation, where kinetic-potential-advection splitting is performed, will be of use.
