Implicit and Higher order time stepping methods

[HTSykora]

Drift:

• [ ] Explicit Runge-Kutta methods for the drift computation
  • [x] Butcher-Tableau
  • [x] RK4
  • [ ] Specialized for RK2 (Heun and Ralston)
  • [ ] Runge—Kutta—Nyström method for 2nd order systems

https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods https://www.sciencedirect.com/science/article/pii/037704279200114O

• [ ] Semi-Implicit
  • [ ] Euler Maruyama: https://arxiv.org/pdf/1907.11408.pdf
• [ ] Implicit method
  • [ ] Implicit Euler

Methods: https://diffeq.sciml.ai/stable/solvers/ode_solve/

Diffusion:

• [ ] Milstein for higher order diffusion integration

Higher order weak approximation:

• [ ] Order 2 weak approximation? Weak order 2 (page 466) + Coefficient functions (page 177):

Source: Peter E. Kloeden - Eckhard Platen: Numerical Solution of Stochastic Differential Equations

[HTSykora]

RK4 produces the same result as the Euler method