Summary of Time Integrators Available In PETSc#
TS Name |
Reference |
Class |
Type |
Order |
---|---|---|---|---|
euler |
forward Euler |
one-step |
explicit |
\(1\) |
ssp |
multistage SSP [Ket08] |
Runge-Kutta |
explicit |
\(\le 4\) |
rk* |
multiscale |
Runge-Kutta |
explicit |
\(\ge 1\) |
beuler |
backward Euler |
one-step |
implicit |
\(1\) |
cn |
Crank-Nicolson |
one-step |
implicit |
\(2\) |
theta* |
theta-method |
one-step |
implicit |
\(\le 2\) |
alpha |
alpha-method [JWH00] |
one-step |
implicit |
\(2\) |
gl |
general linear [BJW07] |
multistep-multistage |
implicit |
\(\le 3\) |
eimex |
extrapolated IMEX [CS10] |
one-step |
IMEX |
\(\ge 1\), adaptive |
arkimex |
IMEX Runge-Kutta |
IMEX |
\(1-5\) |
|
rosw |
Rosenbrock-W |
linearly implicit |
\(1-4\) |
|
glee |
GL with global error |
explicit and implicit |
\(1-3\) |
|
mprk |
Multirate Partitioned Runge-Kutta |
multirate |
explicit |
\(2-3\) |
basicsymplectic |
Basic symplectic integrator for separable Hamiltonian |
semi-implicit Euler and Velocity Verlet |
explicit |
\(1-2\) |
irk |
fully implicit Runge-Kutta |
Gauss-Legrendre |
implicit |
\(2s\) |
- BJW07
J.C. Butcher, Z. Jackiewicz, and W.M. Wright. Error propagation of general linear methods for ordinary differential equations. Journal of Complexity, 23(4-6):560–580, 2007. doi:10.1016/j.jco.2007.01.009.
- CS10
E.M. Constantinescu and A. Sandu. Extrapolated implicit-explicit time stepping. SIAM Journal on Scientific Computing, 31(6):4452–4477, 2010. doi:10.1137/080732833.
- JWH00
K.E. Jansen, C.H. Whiting, and G.M. Hulbert. A generalized-alpha method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Computer Methods in Applied Mechanics and Engineering, 190(3):305–319, 2000.
- Ket08
D.I. Ketcheson. Highly efficient strong stability-preserving Runge–Kutta methods with low-storage implementations. SIAM Journal on Scientific Computing, 30(4):2113–2136, 2008. doi:10.1137/07070485X.