We are concerned with a linear mean-square stability analysis of numerical methods
applied to systems of stochastic differential equations (SDEs) and, in particular, consider the …

In recent years, implicit stochastic Runge–Kutta (SRK) methods have been developed both
for strong and weak approximations. For these methods, the stage values are only given …

We introduce a new family of explicit integrators for stiff Itô stochastic differential equations
(SDEs) of weak order two. These numerical methods belong to the class of one-step …

It is well known that the numerical solution of stiff stochastic ordinary differential equations
leads to a step size reduction when explicit methods are used. This has led to a plethora of …

Abstract Some efficient stochastic Runge–Kutta (SRK) methods for the strong as well as for
the weak approximation of solutions of stochastic differential equations (SDEs) with …

We present and analyze a micro-macro acceleration method for the Monte Carlo simulation
of stochastic differential equations with separation between the (fast) time scale of individual …

We introduce a class of numerical methods for highly oscillatory systems of stochastic
differential equations with general noncommutative noise. We prove global weak error …

An asymptotic stability analysis of numerical methods used for simulating stochastic
differential equations with additive noise is presented. The initial part of the paper is …

A new class of third order Runge-Kutta methods for stochastic differential equations with
additive noise is introduced. In contrast to Platen's method, which to the knowledge of the …

In this paper, we have considered two classes of second-order balanced stochastic Runge–
Kutta methods to multidimensional Itô stochastic differential equations. The control functions …