On mean-square stability properties of a new adaptive stochastic Runge-Kutta method

DOI10.1016/j.cam.2008.05.037zbMath1169.65006OpenAlexW2029755553MaRDI QIDQ1002194

Ali Foroush Bastani, Mohammed Hosseini Ali Abadi

Publication date: 25 February 2009

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2008.05.037

zbMATH Keywords

algorithmstochastic differential equationnumerical experimentsmean-square stabilityadaptive time-steppingstochastic Runge-Kutta methodstep-size selectionforward-backward estimationlocal error estimators

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Ordinary differential equations and systems with randomness (34F05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Error bounds for numerical methods for ordinary differential equations (65L70) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (3)

A variable step-size control algorithm for the weak approximation of stochastic differential equations ⋮ A stepsize control algorithm for SDEs with small noise based on stochastic Runge-Kutta Maruyama methods ⋮ The role of coefficients of a general SPDE on the stability and convergence of a finite difference method

Cites Work

• High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula
• Convergence and stability of implicit Runge-Kutta methods for systems with multiplicative noise
• An adaptive timestepping algorithm for stochastic differential equations.
• \(A\)-stability and stochastic mean-square stability
• A new adaptive Runge-Kutta method for stochastic differential equations
• Mean-square stability properties of an adaptive time-stepping SDE solver
• A General Implicit Splitting for Stabilizing Numerical Simulations of Itô Stochastic Differential Equations
• Mean-Square and Asymptotic Stability of the Stochastic Theta Method
• Stability Analysis of Numerical Schemes for Stochastic Differential Equations
• An adaptive Euler-Maruyama scheme for SDEs: convergence and stability
• Asymptotical mean square stability of an equilibrium point of some linear numerical solutions with multiplicative noise

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