Runge–Kutta Methods (RK2, RK4)

[soran-ghaderi]

ODE Solvers

Classical Explicit Methods

• Explicit Midpoint Method

Embedded (Adaptive) Methods

• Cash–Karp
• Dopri5
• Dopri8

Implicit Methods

• Backward Euler
• Implicit Midpoint Rule
• Trapezoidal Rule
• Kvaerno3, Kvaerno4, Kvaerno5: High-order ESDIRK methods for stiff problems

IMEX (Implicit-Explicit) Methods

• Sil3, KenCarp3, KenCarp4, KenCarp5: Used for "split" problems where part of the system is stiff and part is not.

ODE Specialized Methods

• LeapfrogMidpoint
• ReversibleHeun
• SemiImplicitEuler

SDE Solvers

Basic SDE Solvers

• EulerHeun
• ItoMilstein
• StratonovichMilstein

Stochastic Runge–Kutta (SRK):

• SEA: for additive noise (cheap but low accuracy).
• ShARK, SRA1: Recommended for additive noise.
• SlowRK: For commutative noise.
• SPaRK: for adaptive time-stepping with noncommutative noise.
• GeneralShARK: when the drift is expensive to evaluate

Langevin Solvers

• ALIGN
• ShOULD
• QUICSORT

[phrugsa-limbunlom]

• Backward Euler Backward Euler #137