Diagonally drift-implicit Runge-Kutta methods of weak order one and two for Itô SDEs and stability analysis

Abstract

The class of stochastic Runge-Kutta methods for stochastic differential equations due to Rößler is considered. Coefficient families of diagonally drift-implicit stochastic Runge-Kutta (DDISRK) methods of weak order one and two are calculated. Their asymptotic stability as well as mean-square stability (MS-stability) properties are studied for a linear stochastic test equation with multiplicative noise. The stability functions for the DDISRK methods are determined and their domains of stability are compared to the corresponding domain of stability of the considered test equation. Stability regions are presented for various coefficients of the families of DDISRK methods in order to determine step size restrictions such that the numerical approximation reproduces the characteristics of the solution process.

References in corpus (2)

• Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
• Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations

Cited by in corpus (4)

• A micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations
• Study of micro-macro acceleration schemes for linear slow-fast stochastic differential equations with additive noise
• Truncated Milstein method for non-autonomous stochastic differential equations and its modification
• Stability Analysis and Classification of Runge-Kutta Methods for Index 1 Stochastic Differential-Algebraic Equations with Scalar Noise