Abstract
Stochastic differential equations(SDEs), which appear in various fields of applications, e.g. statistical physics and population dynamics, require another way of calculus than that in usual deterministic case. Among discrete approximations for deterministic differential equations(DDEs), Runge-Kutta method(RK method) is well known. This paper presents a stochastic version of RK method and its applicability for scalar stochastic differential equation. However the local order of convergence of RK scheme in mean-square sense is known to be bounded by 2 in scalar case. We give a way to improve the local order for 3-stage RK scheme.
