Splittings.jl Documentation

Operators splitting package to solve equations of the form

where T and V are differential operators.

The composition algorithm consists in successive solutions of the split equations

and

Alternating the two reduced solution operators $\mathcal{S}_{T}$ and $\mathcal{S}_{V}$ with adequately chosen time increments yields arbitrary order in time for the full solution.

The application of an operator splitting method to a concrete problem is done by using Julia macros:

@Lie( push_t, push_v )

Apply the first order Lie splitting

push_t and push_v are two function calls with
`dt` as argument.

@Strang( push_t, push_v )

Apply the second order Strang splitting

push_t and push_v are two function calls with
`dt` as argument.

@TripleJump( push_t, push_v )

Apply the fourth order Triple Jump splitting

push_t and push_v are two function calls with
`dt` as argument.

@Order6( push_t, push_v )

Apply the sixth order splitting

push_t and push_v are two function calls with
`dt` as argument.

Examples of applications are provided for:

• The linear pendulum problem.
• The Vlasov equation with constant coefficients advection field.
• The non linear Vlasov-Poisson equations in cartesian coordinates.

This code is derived from Fortran and Python codes written by:

• Edwin Chacon Golcher (Institute of Physics of the Czech Academy of Sciences).
• Michel Mehrenberger (Aix-Marseille Université).
• Eric Sonnendrucker (Max-Planck-Institut für Plasmaphysik).