A new adaptive Runge-Kutta method for stochastic differential equations

Authors:
A. Foroush Bastani;S. Mohammad Hosseini
Affiliations:
Department of Mathematics, Tarbiat Modarres University, P.O. Box 14115-175, Tehran, Iran;Department of Mathematics, Tarbiat Modarres University, P.O. Box 14115-175, Tehran, Iran
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 11
Cited 6

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Variable step size control in the numerical solution of stochastic differential equations

SIAM Journal on Applied Mathematics
A formula for steplength control in numerical integration

Journal of Computational and Applied Mathematics
Step size control in the numerical solution of stochastic differential equations

Journal of Computational and Applied Mathematics
Error estimation in Runge-Kutta procedures

Communications of the ACM
Adaptive schemes for the numerical solution of SDEs: a comparison

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

SIAM Journal on Scientific Computing
An adaptive timestepping algorithm for stochastic differential equations

Journal of Computational and Applied Mathematics
Stepsize Control for Mean-Square Numerical Methods for Stochastic Differential Equations with Small Noise

SIAM Journal on Scientific Computing

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

Journal of Computational and Applied Mathematics
The role of coefficients of a general SPDE on the stability and convergence of a finite difference method

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

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

Numerical Algorithms
Original article: Spectral collocation method for stochastic Burgers equation driven by additive noise

Mathematics and Computers in Simulation
A stepsize control algorithm for SDEs with small noise based on stochastic Runge---Kutta Maruyama methods

Numerical Algorithms

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper, we will present a new adaptive time stepping algorithm for strong approximation of stochastic ordinary differential equations. We will employ two different error estimation criteria for drift and diffusion terms of the equation, both of them based on forward and backward moves along the same time step. We will use step size selection mechanisms suitable for each of the two main regimes in the solution behavior, which correspond to domination of the drift-based local error estimator or diffusion-based one. Numerical experiments will show the effectiveness of this approach in the pathwise approximation of several standard test problems.