A stepsize control algorithm for SDEs with small noise based on stochastic Runge---Kutta Maruyama methods

Authors:
A. Valinejad;S. Mohammad Hosseini
Affiliations:
Department of Applied Mathematics, Tarbiat Modares University, Tehran, Iran;Department of Applied Mathematics, Tarbiat Modares University, Tehran, Iran
Venue:
Numerical Algorithms
Year:
2012

Citing 17
Cited 0

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Mean-Square Numerical Methods for Stochastic Differential Equations with Small Noises

SIAM Journal on Scientific Computing
Variable step size control in the numerical solution of stochastic differential equations

SIAM Journal on Applied Mathematics
Step size control in the numerical solution of stochastic differential equations

Journal of Computational and Applied Mathematics
A Variable Stepsize Implementation for Stochastic Differential Equations

SIAM Journal on Scientific Computing
Digital filters in adaptive time-stepping

ACM Transactions on Mathematical Software (TOMS)
Stochastic differential algebraic equations of index 1 and applications in circuit simulation

Journal of Computational and Applied Mathematics
An adaptive timestepping algorithm for stochastic differential equations

Journal of Computational and Applied Mathematics
Adaptive stepsize based on control theory for stochastic differential equations

Journal of Computational and Applied Mathematics
Multistep methods for SDEs and their application to problems with small noise

SIAM Journal on Numerical Analysis
Stepsize Control for Mean-Square Numerical Methods for Stochastic Differential Equations with Small Noise

SIAM Journal on Scientific Computing
A new adaptive Runge-Kutta method for stochastic differential equations

Journal of Computational and Applied Mathematics
On mean-square stability properties of a new adaptive stochastic Runge-Kutta method

Journal of Computational and Applied Mathematics
Time-step selection algorithms: Adaptivity, control, and signal processing

Applied Numerical Mathematics
A variable step-size control algorithm for the weak approximation of stochastic differential equations

Numerical Algorithms
Stochastic Runge-Kutta Methods for Itô SODEs with Small Noise

SIAM Journal on Scientific Computing
Runge-Kutta methods for jump-diffusion differential equations

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

A variable stepsize control algorithm for solution of stochastic differential equations (SDEs) with a small noise parameter 驴 is presented. In order to determine the optimal stepsize for each stage of the algorithm, an estimate of the global error is introduced based on the local error of the Stochastic Runge---Kutta Maruyama (SRKM) methods. Based on the relation of the stepsize and the small noise parameter, the local mean-square stochastic convergence order can be different from stage to stage. Using this relation, a strategy for producing and controlling the stepsize in the numerical integration of SDEs is proposed. Numerical experiments on several standard SDEs with small noise are presented to illustrate the effectiveness of this approach.