List of all Methods
| Method | Order | Explicit | Symmetric | Symplectic | ODE | PODE | HODE | IODE | LODE | SODE | DAE | PDAE | HDAE | IDAE | LDAE |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ERK | missing | ✓ | missing | missing | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
IRK | missing | ✗ | missing | missing | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
DIRK | missing | ✗ | missing | missing | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
EPRK | missing | ✓ | missing | missing | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
IPRK | missing | ✗ | missing | missing | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRK | missing | missing | missing | missing | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
DVRK | missing | ✗ | missing | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
CGVI | missing | ✗ | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
ProjectedMethod | missing | missing | missing | missing | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
HPImidpoint | missing | missing | missing | missing | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
HPItrapezoidal | missing | missing | missing | missing | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
ExplicitEuler | missing | ✓ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
ImplicitEuler | missing | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
ForwardEuler | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
ExplicitEulerRK | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
ExplicitMidpoint | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
Heun2 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
Heun3 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
Kutta3 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
Ralston2 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
Ralston3 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
RK21 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
RK22 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
RK31 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
RK32 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
RK4 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
RK41 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
RK42 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
RK416 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
RK438 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
RK5 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
Runge2 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
SSPRK2 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
SSPRK3 | missing | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
CrankNicolson | missing | ✗ | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
Crouzeix | missing | ✗ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
KraaijevangerSpijker | missing | ✗ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
QinZhang | missing | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
BackwardEuler | missing | ✗ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
ImplicitEulerRK | missing | ✗ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
ImplicitMidpoint | missing | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
SRK3 | missing | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
Gauss | 2s | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIII | 2s-2 | ✗ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIA | 2s-2 | ✗ | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIB | 2s-2 | ✗ | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIC | 2s-2 | ✗ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIID | 2s-2 | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIE | 2s-2 | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIF | 2s | ✗ | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIF̄ | 2s | ✗ | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIG | 2s | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
RadauIA | 2s-1 | ✗ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
RadauIB | 2s-1 | ✗ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
RadauIIA | 2s-1 | ✗ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
RadauIIB | 2s-1 | ✗ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
SymplecticEulerA | 1 | ✓ | ✗ | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
SymplecticEulerB | 1 | ✓ | ✗ | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
PartitionedGauss | 2s | ✗ | missing | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIAIIIB | 2s-2 | missing | missing | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIBIIIA | 2s-2 | missing | missing | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIAIIIĀ | 2s-2 | missing | missing | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIBIIIB̄ | 2s-2 | missing | missing | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIICIIIC̄ | 2s-2 | missing | missing | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIC̄IIIC | 2s-2 | missing | missing | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIDIIID̄ | 2s-2 | missing | missing | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIEIIIĒ | 2s-2 | missing | missing | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIFIIIF̄ | 2s | missing | missing | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIF̄IIIF | 2s | missing | missing | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LobattoIIIGIIIḠ | 2s | missing | missing | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPSRK3 | missing | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKGauss | 2s | missing | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKRadauIIA | 2s-1 | missing | missing | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKRadauIIB | 2s-1 | missing | missing | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIII | 2s-2 | missing | missing | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIA | 2s-2 | missing | missing | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIB | 2s-2 | missing | missing | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIC | 2s-2 | missing | missing | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIID | 2s-2 | missing | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIE | 2s-2 | missing | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIF | 2s | missing | missing | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIF̄ | 2s | missing | missing | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIG | 2s | missing | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIAIIIB | 2s-2 | missing | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIBIIIA | 2s-2 | missing | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIAIIIĀ | 2s-2 | missing | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIBIIIB̄ | 2s-2 | missing | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIICIIIC̄ | 2s-2 | missing | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIC̄IIIC | 2s-2 | missing | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIDIIID̄ | 2s-2 | missing | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIEIIIĒ | 2s-2 | missing | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIFIIIF̄ | 2s | missing | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIF̄IIIF | 2s | missing | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
VPRKLobattoIIIGIIIḠ | 2s | missing | missing | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
HPImidpoint | missing | missing | missing | missing | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
HPItrapezoidal | missing | missing | missing | missing | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
PMVImidpoint | missing | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
PMVItrapezoidal | missing | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
DVIA | 1 | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
DVIB | 1 | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
CMDVI | 2 | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
CTDVI | 2 | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
LieA | 1 | ✓ | missing | missing | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
LieB | 1 | ✓ | missing | missing | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
Strang | 2 | ✓ | missing | missing | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
Marchuk | 2 | ✓ | missing | missing | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
StrangA | 2 | ✓ | missing | missing | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
StrangB | 2 | ✓ | missing | missing | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
McLachlan2 | 2 | ✓ | missing | missing | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
McLachlan4 | 4 | ✓ | missing | missing | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
TripleJump | 4 | ✓ | missing | missing | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
SuzukiFractal | 4 | ✓ | missing | missing | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
ODE Methods
| Method | Order | Explicit | Symmetric | Symplectic |
|---|---|---|---|---|
ERK | missing | ✓ | missing | missing |
IRK | missing | ✗ | missing | missing |
DIRK | missing | ✗ | missing | missing |
ExplicitEuler | missing | ✓ | ✗ | ✗ |
ImplicitEuler | missing | ✗ | ✗ | ✗ |
ForwardEuler | missing | ✓ | ✗ | ✗ |
ExplicitEulerRK | missing | ✓ | ✗ | ✗ |
ExplicitMidpoint | missing | ✓ | ✗ | ✗ |
Heun2 | missing | ✓ | ✗ | ✗ |
Heun3 | missing | ✓ | ✗ | ✗ |
Kutta3 | missing | ✓ | ✗ | ✗ |
Ralston2 | missing | ✓ | ✗ | ✗ |
Ralston3 | missing | ✓ | ✗ | ✗ |
RK21 | missing | ✓ | ✗ | ✗ |
RK22 | missing | ✓ | ✗ | ✗ |
RK31 | missing | ✓ | ✗ | ✗ |
RK32 | missing | ✓ | ✗ | ✗ |
RK4 | missing | ✓ | ✗ | ✗ |
RK41 | missing | ✓ | ✗ | ✗ |
RK42 | missing | ✓ | ✗ | ✗ |
RK416 | missing | ✓ | ✗ | ✗ |
RK438 | missing | ✓ | ✗ | ✗ |
RK5 | missing | ✓ | ✗ | ✗ |
Runge2 | missing | ✓ | ✗ | ✗ |
SSPRK2 | missing | ✓ | ✗ | ✗ |
SSPRK3 | missing | ✓ | ✗ | ✗ |
CrankNicolson | missing | ✗ | ✓ | ✗ |
Crouzeix | missing | ✗ | ✗ | ✗ |
KraaijevangerSpijker | missing | ✗ | ✗ | ✗ |
QinZhang | missing | ✗ | ✓ | ✓ |
BackwardEuler | missing | ✗ | ✗ | ✗ |
ImplicitEulerRK | missing | ✗ | ✗ | ✗ |
ImplicitMidpoint | missing | ✗ | ✓ | ✓ |
SRK3 | missing | ✗ | ✓ | ✓ |
Gauss | 2s | ✗ | ✓ | ✓ |
LobattoIII | 2s-2 | ✗ | ✗ | ✗ |
LobattoIIIA | 2s-2 | ✗ | ✓ | ✗ |
LobattoIIIB | 2s-2 | ✗ | ✓ | ✗ |
LobattoIIIC | 2s-2 | ✗ | ✗ | ✗ |
LobattoIIID | 2s-2 | ✗ | ✓ | ✓ |
LobattoIIIE | 2s-2 | ✗ | ✓ | ✓ |
LobattoIIIF | 2s | ✗ | ✓ | ✗ |
LobattoIIIF̄ | 2s | ✗ | ✓ | ✗ |
LobattoIIIG | 2s | ✗ | ✓ | ✓ |
RadauIA | 2s-1 | ✗ | ✗ | ✗ |
RadauIB | 2s-1 | ✗ | ✗ | ✗ |
RadauIIA | 2s-1 | ✗ | ✗ | ✗ |
RadauIIB | 2s-1 | ✗ | ✗ | ✗ |
PODE Methods
| Method | Order | Explicit | Symmetric | Symplectic |
|---|---|---|---|---|
ERK | missing | ✓ | missing | missing |
IRK | missing | ✗ | missing | missing |
DIRK | missing | ✗ | missing | missing |
EPRK | missing | ✓ | missing | missing |
IPRK | missing | ✗ | missing | missing |
ForwardEuler | missing | ✓ | ✗ | ✗ |
ExplicitEulerRK | missing | ✓ | ✗ | ✗ |
ExplicitMidpoint | missing | ✓ | ✗ | ✗ |
Heun2 | missing | ✓ | ✗ | ✗ |
Heun3 | missing | ✓ | ✗ | ✗ |
Kutta3 | missing | ✓ | ✗ | ✗ |
Ralston2 | missing | ✓ | ✗ | ✗ |
Ralston3 | missing | ✓ | ✗ | ✗ |
RK21 | missing | ✓ | ✗ | ✗ |
RK22 | missing | ✓ | ✗ | ✗ |
RK31 | missing | ✓ | ✗ | ✗ |
RK32 | missing | ✓ | ✗ | ✗ |
RK4 | missing | ✓ | ✗ | ✗ |
RK41 | missing | ✓ | ✗ | ✗ |
RK42 | missing | ✓ | ✗ | ✗ |
RK416 | missing | ✓ | ✗ | ✗ |
RK438 | missing | ✓ | ✗ | ✗ |
RK5 | missing | ✓ | ✗ | ✗ |
Runge2 | missing | ✓ | ✗ | ✗ |
SSPRK2 | missing | ✓ | ✗ | ✗ |
SSPRK3 | missing | ✓ | ✗ | ✗ |
CrankNicolson | missing | ✗ | ✓ | ✗ |
Crouzeix | missing | ✗ | ✗ | ✗ |
KraaijevangerSpijker | missing | ✗ | ✗ | ✗ |
QinZhang | missing | ✗ | ✓ | ✓ |
BackwardEuler | missing | ✗ | ✗ | ✗ |
ImplicitEulerRK | missing | ✗ | ✗ | ✗ |
ImplicitMidpoint | missing | ✗ | ✓ | ✓ |
SRK3 | missing | ✗ | ✓ | ✓ |
Gauss | 2s | ✗ | ✓ | ✓ |
LobattoIII | 2s-2 | ✗ | ✗ | ✗ |
LobattoIIIA | 2s-2 | ✗ | ✓ | ✗ |
LobattoIIIB | 2s-2 | ✗ | ✓ | ✗ |
LobattoIIIC | 2s-2 | ✗ | ✗ | ✗ |
LobattoIIID | 2s-2 | ✗ | ✓ | ✓ |
LobattoIIIE | 2s-2 | ✗ | ✓ | ✓ |
LobattoIIIF | 2s | ✗ | ✓ | ✗ |
LobattoIIIF̄ | 2s | ✗ | ✓ | ✗ |
LobattoIIIG | 2s | ✗ | ✓ | ✓ |
RadauIA | 2s-1 | ✗ | ✗ | ✗ |
RadauIB | 2s-1 | ✗ | ✗ | ✗ |
RadauIIA | 2s-1 | ✗ | ✗ | ✗ |
RadauIIB | 2s-1 | ✗ | ✗ | ✗ |
SymplecticEulerA | 1 | ✓ | ✗ | ✓ |
SymplecticEulerB | 1 | ✓ | ✗ | ✓ |
PartitionedGauss | 2s | ✗ | missing | ✓ |
LobattoIIIAIIIB | 2s-2 | missing | missing | ✓ |
LobattoIIIBIIIA | 2s-2 | missing | missing | ✓ |
LobattoIIIAIIIĀ | 2s-2 | missing | missing | ✓ |
LobattoIIIBIIIB̄ | 2s-2 | missing | missing | ✓ |
LobattoIIICIIIC̄ | 2s-2 | missing | missing | ✓ |
LobattoIIIC̄IIIC | 2s-2 | missing | missing | ✓ |
LobattoIIIDIIID̄ | 2s-2 | missing | missing | ✓ |
LobattoIIIEIIIĒ | 2s-2 | missing | missing | ✓ |
LobattoIIIFIIIF̄ | 2s | missing | missing | ✓ |
LobattoIIIF̄IIIF | 2s | missing | missing | ✓ |
LobattoIIIGIIIḠ | 2s | missing | missing | ✓ |
HODE Methods
| Method | Order | Explicit | Symmetric | Symplectic |
|---|---|---|---|---|
ERK | missing | ✓ | missing | missing |
IRK | missing | ✗ | missing | missing |
DIRK | missing | ✗ | missing | missing |
EPRK | missing | ✓ | missing | missing |
IPRK | missing | ✗ | missing | missing |
ForwardEuler | missing | ✓ | ✗ | ✗ |
ExplicitEulerRK | missing | ✓ | ✗ | ✗ |
ExplicitMidpoint | missing | ✓ | ✗ | ✗ |
Heun2 | missing | ✓ | ✗ | ✗ |
Heun3 | missing | ✓ | ✗ | ✗ |
Kutta3 | missing | ✓ | ✗ | ✗ |
Ralston2 | missing | ✓ | ✗ | ✗ |
Ralston3 | missing | ✓ | ✗ | ✗ |
RK21 | missing | ✓ | ✗ | ✗ |
RK22 | missing | ✓ | ✗ | ✗ |
RK31 | missing | ✓ | ✗ | ✗ |
RK32 | missing | ✓ | ✗ | ✗ |
RK4 | missing | ✓ | ✗ | ✗ |
RK41 | missing | ✓ | ✗ | ✗ |
RK42 | missing | ✓ | ✗ | ✗ |
RK416 | missing | ✓ | ✗ | ✗ |
RK438 | missing | ✓ | ✗ | ✗ |
RK5 | missing | ✓ | ✗ | ✗ |
Runge2 | missing | ✓ | ✗ | ✗ |
SSPRK2 | missing | ✓ | ✗ | ✗ |
SSPRK3 | missing | ✓ | ✗ | ✗ |
CrankNicolson | missing | ✗ | ✓ | ✗ |
Crouzeix | missing | ✗ | ✗ | ✗ |
KraaijevangerSpijker | missing | ✗ | ✗ | ✗ |
QinZhang | missing | ✗ | ✓ | ✓ |
BackwardEuler | missing | ✗ | ✗ | ✗ |
ImplicitEulerRK | missing | ✗ | ✗ | ✗ |
ImplicitMidpoint | missing | ✗ | ✓ | ✓ |
SRK3 | missing | ✗ | ✓ | ✓ |
Gauss | 2s | ✗ | ✓ | ✓ |
LobattoIII | 2s-2 | ✗ | ✗ | ✗ |
LobattoIIIA | 2s-2 | ✗ | ✓ | ✗ |
LobattoIIIB | 2s-2 | ✗ | ✓ | ✗ |
LobattoIIIC | 2s-2 | ✗ | ✗ | ✗ |
LobattoIIID | 2s-2 | ✗ | ✓ | ✓ |
LobattoIIIE | 2s-2 | ✗ | ✓ | ✓ |
LobattoIIIF | 2s | ✗ | ✓ | ✗ |
LobattoIIIF̄ | 2s | ✗ | ✓ | ✗ |
LobattoIIIG | 2s | ✗ | ✓ | ✓ |
RadauIA | 2s-1 | ✗ | ✗ | ✗ |
RadauIB | 2s-1 | ✗ | ✗ | ✗ |
RadauIIA | 2s-1 | ✗ | ✗ | ✗ |
RadauIIB | 2s-1 | ✗ | ✗ | ✗ |
SymplecticEulerA | 1 | ✓ | ✗ | ✓ |
SymplecticEulerB | 1 | ✓ | ✗ | ✓ |
PartitionedGauss | 2s | ✗ | missing | ✓ |
LobattoIIIAIIIB | 2s-2 | missing | missing | ✓ |
LobattoIIIBIIIA | 2s-2 | missing | missing | ✓ |
LobattoIIIAIIIĀ | 2s-2 | missing | missing | ✓ |
LobattoIIIBIIIB̄ | 2s-2 | missing | missing | ✓ |
LobattoIIICIIIC̄ | 2s-2 | missing | missing | ✓ |
LobattoIIIC̄IIIC | 2s-2 | missing | missing | ✓ |
LobattoIIIDIIID̄ | 2s-2 | missing | missing | ✓ |
LobattoIIIEIIIĒ | 2s-2 | missing | missing | ✓ |
LobattoIIIFIIIF̄ | 2s | missing | missing | ✓ |
LobattoIIIF̄IIIF | 2s | missing | missing | ✓ |
LobattoIIIGIIIḠ | 2s | missing | missing | ✓ |
IODE Methods
| Method | Order | Explicit | Symmetric | Symplectic |
|---|---|---|---|---|
ERK | missing | ✓ | missing | missing |
IRK | missing | ✗ | missing | missing |
DIRK | missing | ✗ | missing | missing |
EPRK | missing | ✓ | missing | missing |
IPRK | missing | ✗ | missing | missing |
VPRK | missing | missing | missing | missing |
CGVI | missing | ✗ | missing | ✓ |
HPImidpoint | missing | missing | missing | missing |
HPItrapezoidal | missing | missing | missing | missing |
ForwardEuler | missing | ✓ | ✗ | ✗ |
ExplicitEulerRK | missing | ✓ | ✗ | ✗ |
ExplicitMidpoint | missing | ✓ | ✗ | ✗ |
Heun2 | missing | ✓ | ✗ | ✗ |
Heun3 | missing | ✓ | ✗ | ✗ |
Kutta3 | missing | ✓ | ✗ | ✗ |
Ralston2 | missing | ✓ | ✗ | ✗ |
Ralston3 | missing | ✓ | ✗ | ✗ |
RK21 | missing | ✓ | ✗ | ✗ |
RK22 | missing | ✓ | ✗ | ✗ |
RK31 | missing | ✓ | ✗ | ✗ |
RK32 | missing | ✓ | ✗ | ✗ |
RK4 | missing | ✓ | ✗ | ✗ |
RK41 | missing | ✓ | ✗ | ✗ |
RK42 | missing | ✓ | ✗ | ✗ |
RK416 | missing | ✓ | ✗ | ✗ |
RK438 | missing | ✓ | ✗ | ✗ |
RK5 | missing | ✓ | ✗ | ✗ |
Runge2 | missing | ✓ | ✗ | ✗ |
SSPRK2 | missing | ✓ | ✗ | ✗ |
SSPRK3 | missing | ✓ | ✗ | ✗ |
CrankNicolson | missing | ✗ | ✓ | ✗ |
Crouzeix | missing | ✗ | ✗ | ✗ |
KraaijevangerSpijker | missing | ✗ | ✗ | ✗ |
QinZhang | missing | ✗ | ✓ | ✓ |
BackwardEuler | missing | ✗ | ✗ | ✗ |
ImplicitEulerRK | missing | ✗ | ✗ | ✗ |
ImplicitMidpoint | missing | ✗ | ✓ | ✓ |
SRK3 | missing | ✗ | ✓ | ✓ |
Gauss | 2s | ✗ | ✓ | ✓ |
LobattoIII | 2s-2 | ✗ | ✗ | ✗ |
LobattoIIIA | 2s-2 | ✗ | ✓ | ✗ |
LobattoIIIB | 2s-2 | ✗ | ✓ | ✗ |
LobattoIIIC | 2s-2 | ✗ | ✗ | ✗ |
LobattoIIID | 2s-2 | ✗ | ✓ | ✓ |
LobattoIIIE | 2s-2 | ✗ | ✓ | ✓ |
LobattoIIIF | 2s | ✗ | ✓ | ✗ |
LobattoIIIF̄ | 2s | ✗ | ✓ | ✗ |
LobattoIIIG | 2s | ✗ | ✓ | ✓ |
RadauIA | 2s-1 | ✗ | ✗ | ✗ |
RadauIB | 2s-1 | ✗ | ✗ | ✗ |
RadauIIA | 2s-1 | ✗ | ✗ | ✗ |
RadauIIB | 2s-1 | ✗ | ✗ | ✗ |
SymplecticEulerA | 1 | ✓ | ✗ | ✓ |
SymplecticEulerB | 1 | ✓ | ✗ | ✓ |
PartitionedGauss | 2s | ✗ | missing | ✓ |
LobattoIIIAIIIB | 2s-2 | missing | missing | ✓ |
LobattoIIIBIIIA | 2s-2 | missing | missing | ✓ |
LobattoIIIAIIIĀ | 2s-2 | missing | missing | ✓ |
LobattoIIIBIIIB̄ | 2s-2 | missing | missing | ✓ |
LobattoIIICIIIC̄ | 2s-2 | missing | missing | ✓ |
LobattoIIIC̄IIIC | 2s-2 | missing | missing | ✓ |
LobattoIIIDIIID̄ | 2s-2 | missing | missing | ✓ |
LobattoIIIEIIIĒ | 2s-2 | missing | missing | ✓ |
LobattoIIIFIIIF̄ | 2s | missing | missing | ✓ |
LobattoIIIF̄IIIF | 2s | missing | missing | ✓ |
LobattoIIIGIIIḠ | 2s | missing | missing | ✓ |
VPSRK3 | missing | ✗ | ✓ | ✓ |
VPRKGauss | 2s | missing | missing | ✓ |
VPRKRadauIIA | 2s-1 | missing | missing | ✗ |
VPRKRadauIIB | 2s-1 | missing | missing | ✗ |
VPRKLobattoIII | 2s-2 | missing | missing | ✗ |
VPRKLobattoIIIA | 2s-2 | missing | missing | ✗ |
VPRKLobattoIIIB | 2s-2 | missing | missing | ✗ |
VPRKLobattoIIIC | 2s-2 | missing | missing | ✗ |
VPRKLobattoIIID | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIE | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIF | 2s | missing | missing | ✗ |
VPRKLobattoIIIF̄ | 2s | missing | missing | ✗ |
VPRKLobattoIIIG | 2s | missing | missing | ✓ |
VPRKLobattoIIIAIIIB | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIBIIIA | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIAIIIĀ | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIBIIIB̄ | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIICIIIC̄ | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIC̄IIIC | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIDIIID̄ | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIEIIIĒ | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIFIIIF̄ | 2s | missing | missing | ✓ |
VPRKLobattoIIIF̄IIIF | 2s | missing | missing | ✓ |
VPRKLobattoIIIGIIIḠ | 2s | missing | missing | ✓ |
HPImidpoint | missing | missing | missing | missing |
HPItrapezoidal | missing | missing | missing | missing |
PMVImidpoint | missing | ✗ | ✓ | ✓ |
PMVItrapezoidal | missing | ✗ | ✓ | ✓ |
LODE Methods
| Method | Order | Explicit | Symmetric | Symplectic |
|---|---|---|---|---|
ERK | missing | ✓ | missing | missing |
IRK | missing | ✗ | missing | missing |
DIRK | missing | ✗ | missing | missing |
EPRK | missing | ✓ | missing | missing |
IPRK | missing | ✗ | missing | missing |
VPRK | missing | missing | missing | missing |
DVRK | missing | ✗ | missing | ✓ |
CGVI | missing | ✗ | missing | ✓ |
HPImidpoint | missing | missing | missing | missing |
HPItrapezoidal | missing | missing | missing | missing |
ForwardEuler | missing | ✓ | ✗ | ✗ |
ExplicitEulerRK | missing | ✓ | ✗ | ✗ |
ExplicitMidpoint | missing | ✓ | ✗ | ✗ |
Heun2 | missing | ✓ | ✗ | ✗ |
Heun3 | missing | ✓ | ✗ | ✗ |
Kutta3 | missing | ✓ | ✗ | ✗ |
Ralston2 | missing | ✓ | ✗ | ✗ |
Ralston3 | missing | ✓ | ✗ | ✗ |
RK21 | missing | ✓ | ✗ | ✗ |
RK22 | missing | ✓ | ✗ | ✗ |
RK31 | missing | ✓ | ✗ | ✗ |
RK32 | missing | ✓ | ✗ | ✗ |
RK4 | missing | ✓ | ✗ | ✗ |
RK41 | missing | ✓ | ✗ | ✗ |
RK42 | missing | ✓ | ✗ | ✗ |
RK416 | missing | ✓ | ✗ | ✗ |
RK438 | missing | ✓ | ✗ | ✗ |
RK5 | missing | ✓ | ✗ | ✗ |
Runge2 | missing | ✓ | ✗ | ✗ |
SSPRK2 | missing | ✓ | ✗ | ✗ |
SSPRK3 | missing | ✓ | ✗ | ✗ |
CrankNicolson | missing | ✗ | ✓ | ✗ |
Crouzeix | missing | ✗ | ✗ | ✗ |
KraaijevangerSpijker | missing | ✗ | ✗ | ✗ |
QinZhang | missing | ✗ | ✓ | ✓ |
BackwardEuler | missing | ✗ | ✗ | ✗ |
ImplicitEulerRK | missing | ✗ | ✗ | ✗ |
ImplicitMidpoint | missing | ✗ | ✓ | ✓ |
SRK3 | missing | ✗ | ✓ | ✓ |
Gauss | 2s | ✗ | ✓ | ✓ |
LobattoIII | 2s-2 | ✗ | ✗ | ✗ |
LobattoIIIA | 2s-2 | ✗ | ✓ | ✗ |
LobattoIIIB | 2s-2 | ✗ | ✓ | ✗ |
LobattoIIIC | 2s-2 | ✗ | ✗ | ✗ |
LobattoIIID | 2s-2 | ✗ | ✓ | ✓ |
LobattoIIIE | 2s-2 | ✗ | ✓ | ✓ |
LobattoIIIF | 2s | ✗ | ✓ | ✗ |
LobattoIIIF̄ | 2s | ✗ | ✓ | ✗ |
LobattoIIIG | 2s | ✗ | ✓ | ✓ |
RadauIA | 2s-1 | ✗ | ✗ | ✗ |
RadauIB | 2s-1 | ✗ | ✗ | ✗ |
RadauIIA | 2s-1 | ✗ | ✗ | ✗ |
RadauIIB | 2s-1 | ✗ | ✗ | ✗ |
SymplecticEulerA | 1 | ✓ | ✗ | ✓ |
SymplecticEulerB | 1 | ✓ | ✗ | ✓ |
PartitionedGauss | 2s | ✗ | missing | ✓ |
LobattoIIIAIIIB | 2s-2 | missing | missing | ✓ |
LobattoIIIBIIIA | 2s-2 | missing | missing | ✓ |
LobattoIIIAIIIĀ | 2s-2 | missing | missing | ✓ |
LobattoIIIBIIIB̄ | 2s-2 | missing | missing | ✓ |
LobattoIIICIIIC̄ | 2s-2 | missing | missing | ✓ |
LobattoIIIC̄IIIC | 2s-2 | missing | missing | ✓ |
LobattoIIIDIIID̄ | 2s-2 | missing | missing | ✓ |
LobattoIIIEIIIĒ | 2s-2 | missing | missing | ✓ |
LobattoIIIFIIIF̄ | 2s | missing | missing | ✓ |
LobattoIIIF̄IIIF | 2s | missing | missing | ✓ |
LobattoIIIGIIIḠ | 2s | missing | missing | ✓ |
VPSRK3 | missing | ✗ | ✓ | ✓ |
VPRKGauss | 2s | missing | missing | ✓ |
VPRKRadauIIA | 2s-1 | missing | missing | ✗ |
VPRKRadauIIB | 2s-1 | missing | missing | ✗ |
VPRKLobattoIII | 2s-2 | missing | missing | ✗ |
VPRKLobattoIIIA | 2s-2 | missing | missing | ✗ |
VPRKLobattoIIIB | 2s-2 | missing | missing | ✗ |
VPRKLobattoIIIC | 2s-2 | missing | missing | ✗ |
VPRKLobattoIIID | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIE | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIF | 2s | missing | missing | ✗ |
VPRKLobattoIIIF̄ | 2s | missing | missing | ✗ |
VPRKLobattoIIIG | 2s | missing | missing | ✓ |
VPRKLobattoIIIAIIIB | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIBIIIA | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIAIIIĀ | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIBIIIB̄ | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIICIIIC̄ | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIC̄IIIC | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIDIIID̄ | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIEIIIĒ | 2s-2 | missing | missing | ✓ |
VPRKLobattoIIIFIIIF̄ | 2s | missing | missing | ✓ |
VPRKLobattoIIIF̄IIIF | 2s | missing | missing | ✓ |
VPRKLobattoIIIGIIIḠ | 2s | missing | missing | ✓ |
HPImidpoint | missing | missing | missing | missing |
HPItrapezoidal | missing | missing | missing | missing |
PMVImidpoint | missing | ✗ | ✓ | ✓ |
PMVItrapezoidal | missing | ✗ | ✓ | ✓ |
DVIA | 1 | ✗ | ✗ | ✓ |
DVIB | 1 | ✗ | ✗ | ✓ |
CMDVI | 2 | ✗ | ✓ | ✓ |
CTDVI | 2 | ✗ | ✓ | ✓ |
SODE Methods
| Method | Order | Explicit | Symmetric | Symplectic |
|---|---|---|---|---|
LieA | 1 | ✓ | missing | missing |
LieB | 1 | ✓ | missing | missing |
Strang | 2 | ✓ | missing | missing |
Marchuk | 2 | ✓ | missing | missing |
StrangA | 2 | ✓ | missing | missing |
StrangB | 2 | ✓ | missing | missing |
McLachlan2 | 2 | ✓ | missing | missing |
McLachlan4 | 4 | ✓ | missing | missing |
TripleJump | 4 | ✓ | missing | missing |
SuzukiFractal | 4 | ✓ | missing | missing |