Split ODE Problems

Split ODE Problems

Mathematical Specification of a Split ODE Problem

To define a SplitODEProblem, you simply need to give a tuple of functions $(f_1,f_2,\ldots,f_n)$ and the initial condition $u₀$ which define an ODE:

\[\frac{du}{dt} = f_1(t,u) + f_2(t,u) + \ldots + f_n(t,u)\]

f should be specified as f(t,u) (or in-place as f(t,u,du)), and u₀ should be an AbstractArray (or number) whose geometry matches the desired geometry of u. Note that we are not limited to numbers or vectors for u₀; one is allowed to provide u₀ as arbitrary matrices / higher dimension tensors as well.

Many splits are at least partially linear. For how to define a function as linear, see the documentation for the DiffEqOperators.