**petsc-main 2021-04-20**

# 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)

References
E. Constantinescu and A. Sandu, Extrapolated implicit-explicit time stepping, SIAM Journal on Scientific
Computing, 31 (2010), pp. 4452-4477.

### See Also

TSCreate(), TS, TSSetType(), TSEIMEXSetMaxRows(), TSEIMEXSetRowCol(), TSEIMEXSetOrdAdapt()

### Level

beginner

### Location

src/ts/impls/eimex/eimex.c

Index of all TS routines

Table of Contents for all manual pages

Index of all manual pages