Some new stochastic Runge–Kutta (SRK) methods for the strong approximation of solutions
of stochastic differential equations (SDEs) with improved efficiency are introduced. Their …

The numerical solution of stochastic partial differential equations (SPDEs) is at a stage of
development roughly similar to that of stochastic ordinary differential equations (SODEs) in …

A new class of stochastic Runge–Kutta methods for the weak approximation of the solution
of Itô stochastic differential equation systems with a multidimensional Wiener process is …

A general class of stochastic Runge-Kutta methods for the weak approximation of Itô and
Stratonovich stochastic differential equations with a multi-dimensional Wiener process is …

In this paper we describe a general framework for deriving modified equations for stochastic
differential equations (SDEs) with respect to weak convergence. Modified equations are …

The solution of a parabolic stochastic partial differential equation (SPDE) driven by an
infinite-dimensional Brownian motion is in general not a semi-martingale anymore and does …

We derive a new methodology for the construction of high-order integrators for sampling the
invariant measure of ergodic stochastic differential equations with dynamics constrained on …

A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation
systems wrt a one-dimensional Wiener process is introduced. The colored rooted tree …

While backward error analysis does not generalise straightforwardly to the strong and weak
approximation of stochastic differential equations, it extends for the sampling of ergodic …

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 …