:orphan: # TSEIMEX Time stepping with Extrapolated IMEX methods. These methods are intended for problems with well-separated time scales, especially when a slow scale is strongly nonlinear such that it is expensive to solve with a fully implicit method. The user should provide the stiff part of the equation using `TSSetIFunction()` and the non-stiff part with `TSSetRHSFunction()`. ## Notes The default is a 3-stage scheme, it can be changed with `TSEIMEXSetMaxRows()` or -ts_eimex_max_rows This method currently only works with ODE, for which the stiff part G(t,X,Xdot) has the form Xdot + Ghat(t,X). The general system is written as G(t,X,Xdot) = F(t,X) where G represents the stiff part and F represents the non-stiff part. The user should provide the stiff part of the equation using TSSetIFunction() and the non-stiff part with `TSSetRHSFunction()`. This method is designed to be linearly implicit on G and can use an approximate and lagged Jacobian. Another common form for the system is y'=f(x)+g(x) The relationship between F,G and f,g is G = y'-g(x), F = f(x) ## Reference - ***[1] -*** E. Constantinescu and A. Sandu, Extrapolated implicit-explicit time stepping, SIAM Journal on Scientific Computing, 31 (2010), pp. 4452-4477. ## See Also [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSEIMEXSetMaxRows()`, `TSEIMEXSetRowCol()`, `TSEIMEXSetOrdAdapt()`, `TSType` ## Level beginner ## Location src/ts/impls/eimex/eimex.c --- [Edit on GitLab](https://gitlab.com/petsc/petsc/-/edit/release/src/ts/impls/eimex/eimex.c) [Index of all TS routines](index.md) [Table of Contents for all manual pages](/manualpages/index.md) [Index of all manual pages](/manualpages/singleindex.md)