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 SplitODEProblem 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

SplitEuler: 1st order fully explicit method. Used for testing accuracy of splits.
KenCarp3: An A-L stable stiffly-accurate 3rd order ESDIRK method
KenCarp4: An A-L stable stiffly-accurate 4rd order ESDIRK method
KenCarp5: An A-L stable stiffly-accurate 5rd order ESDIRK method

Sundials.jl

ARKODE: An additive Runge-Kutta method. Not yet implemented.

Semilinear ODE

The Semilinear ODE is a split ODEProblem with one linear operator and one function:

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

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

GenericIIF1 - First order Implicit Integrating Factor method. Fixed timestepping only.
GenericIIF2 - Second order Implicit Integrating Factor method. Fixed timestepping only.
ETD1 - First order Exponential Time Differencing method. Not yet implemented.
ETD2 - Second order Exponential Time Differencing method. Not yet implemented.
LawsonEuler - First order exponential Euler scheme. Fixed timestepping only.
NorsettEuler - First order exponential-RK scheme. Fixed timestepping only.

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