Split ODE Solvers

Split ODE Solvers

The solvers which are available for a SplitODEProblem depend on the input linearity and number of components. Each solver has functional form (or many) that it allows.

Implicit-Explicit (IMEX) ODE

The Implicit-Explicit (IMEX) ODE is a split ODEProblem with two functions:

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

where the first function is the stiff part and the second function is the non-stiff part (implicit integration on f1, explicit integration on f2).

The appropriate algorithms for this form are:

OrdinaryDiffEq.jl

Sundials.jl

Semilinear ODE

The Semilinear ODE is a split ODEProblem with two functions:

\[\frac{du}{dt} = Au + f(t,u)\]

where the first function is a constant (not time dependent)AbstractDiffEqOperator and the second part is a (nonlinear) function. ../../features/diffeq_operator.html.

The appropriate algorithms for this form are:

OrdinaryDiffEq.jl

Note that the generic algorithms allow for a choice of nlsolve.