Weak first- or second-order implicit Runge–Kutta methods for stochastic differential equations with a scalar Wiener process

摘要

New fully implicit stochastic Runge–Kutta schemes of weak order 1 or 2 are proposed for stochastic differential equations with sufficiently smooth drift and diffusion coefficients and a scalar Wiener process, which are derivative-free and which are A-stable in mean square for a linear test equation in some general settings. They are sought in a transparent way and their convergence order and stability properties are confirmed in numerical experiments.