Modify the Improved Euler scheme to integrate stochastic differential equations
Provides an accessible entry-level numerical method for stochastic differential equations, building on the deterministic Improved Euler/Heun method.
The paper presents a new Runge-Kutta scheme for stochastic differential equations, demonstrating first-order strong convergence for both Ito and Stratonovich interpretations through numerical examples and proof using Ito integrals.
A practical and new Runge--Kutta numerical scheme for stochastic differential equations is explored. Numerical examples demonstrate the strong convergence of the method. The first order strong convergence is then proved using Ito integrals for both Ito and Stratonovich interpretations. As a straightforward modification of the deterministic Improved Euler/Heun method, the method is a good entry level scheme for stochastic differential equations, especially in conjunction with Higham's introduction [SIAM Review, 43:525--546, 2001].