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

Authors:
Kristian Debrabant;Andreas Rößler
Affiliations:
Technische Universität Darmstadt, Fachbereich Mathematik, Schlossgartenstr. 7, D-64289 Darmstadt, Germany;Technische Universität Darmstadt, Fachbereich Mathematik, Schlossgartenstr. 7, D-64289 Darmstadt, Germany
Venue:
Applied Numerical Mathematics
Year:
2009

Citing 12
Cited 4

A-stability of Runge-Kutta methods for systems with additive noise

BIT
Stability Analysis of Numerical Schemes for Stochastic Differential Equations

SIAM Journal on Numerical Analysis
Balanced Implicit Methods for Stiff Stochastic Systems

SIAM Journal on Numerical Analysis
A General Implicit Splitting for Stabilizing Numerical Simulations of Itô Stochastic Differential Equations

SIAM Journal on Numerical Analysis
Numerical solutions of stochastic differential equations — implementation and stability issues

Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Weak Second Order Conditions for Stochastic Runge--Kutta Methods

SIAM Journal on Scientific Computing
Mean-Square and Asymptotic Stability of the Stochastic Theta Method

SIAM Journal on Numerical Analysis
Runge-Kutta methods for Stratonovich stochastic differential equation systems with commutative noise

Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Mean-square stability of second-order Runge-Kutta methods for stochastic differential equations

Journal of Computational and Applied Mathematics
Weak first- or second-order implicit Runge-Kutta methods for stochastic differential equations with a scalar Wiener process

Journal of Computational and Applied Mathematics
Families of efficient second order Runge--Kutta methods for the weak approximation of Itô stochastic differential equations

Applied Numerical Mathematics
B-Series Analysis of Stochastic Runge-Kutta Methods That Use an Iterative Scheme to Compute Their Internal Stage Values

SIAM Journal on Numerical Analysis

On the stability of some second order numerical methods for weak approximation of Itô SDEs

Numerical Algorithms
Weak second order S-ROCK methods for Stratonovich stochastic differential equations

Journal of Computational and Applied Mathematics
A structural analysis of asymptotic mean-square stability for multi-dimensional linear stochastic differential systems

Applied Numerical Mathematics
Linear mean-square stability analysis of weak order 2.0 semi-implicit Taylor schemes for scalar stochastic differential equations

Applied Numerical Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

The class of stochastic Runge-Kutta methods for stochastic differential equations due to Roszler 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.