time_integration.md

[Time integration methods](@id time-integration)

Trixi is compatible with the SciML ecosystem for ordinary differential equations. In particular, explicit Runge-Kutta methods from OrdinaryDiffEq.jl are tested extensively. Interesting classes of time integration schemes are

• Explicit low-storage Runge-Kutta methods
• Strong stability preserving methods

Some common options for solve from OrdinaryDiffEq.jl are the following. Further documentation can be found in the SciML docs.

• If you use a fixed time step method like CarpenterKennedy2N54, you need to pass a time step as dt=.... If you use a StepsizeCallback, the value passed as dt=... is irrelevant since it will be overwritten by the StepsizeCallback.
• You should usually set save_everystep=false. Otherwise, OrdinaryDiffEq.jl will (try to) save the numerical solution after every time step in RAM (until you run out of memory or start to swap).
• You can set the maximal number of time steps via maxiters=....
• SSP methods and 2N low-storage methods from OrdinaryDiffEq.jl support stage_limiter!s and step_limiter!s, e.g. PositivityPreservingLimiterZhangShu from Trixi.

!!! note "Number of rhs! calls" If you use explicit Runge-Kutta methods from OrdinaryDiffEq.jl, the total number of rhs! calls can be (slightly) bigger than the number of steps times the number of stages, e.g. to allow for interpolation (dense output), root-finding for continuous callbacks, and error-based time step control. In general, you often should not need to worry about this if you use Trixi.