Three-stage stochastic Runge-Kutta methods for stochastic differential equations
type: Item
instance of: scholarly article
title: Three-stage stochastic Runge-Kutta methods for stochastic differential equations
zbMATH Open document ID: 1181.65016
author: Peng Wang
published in: Journal of Computational and Applied Mathematics
publication date: 2008-11-18T00:00:00Z
review text: Two stochastic Runge-Kutta methods with strong order of convergence 1 (one a three-stage explicit scheme, the other a three-stage semi-implicit scheme) are devised for approximating the strong solution of the \(m\)-dimensional Stratonovich stochastic differential equation \[ dy(t) =f(y(t))dt+g(y(t))\circ dW(t),\quad y(t_0)=y_0 \] where \(W(t)\) is a Wiener process. Their respective regions of MS-stability are studied. Numerical results are summarized for two examples to demonstrate the favorable accuracy of the methods.
reviewed by: Melvin D. Lax
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 5368371
zbMATH Keywords: stochastic Runge-Kutta methods
zbMATH Keywords: numerical stability
zbMATH Keywords: order condition
zbMATH Keywords: principal error coefficient
zbMATH Keywords: Stratonovich stochastic differential equation
zbMATH Keywords: Wiener process
zbMATH Keywords: numerical results
MaRDI profile type: Publication
full work available at URL: j.cam.2007.11.001
OpenAlex ID: W2057638127
cites work: Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
cites work: High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations
cites work: A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations
cites work: Order conditions of stochastic Runge--Kutta methods by B-series
cites work: Q4725642
cites work: Q4732346
cites work: An algorithmic introduction to numerical simulation of stochastic differential equations
cites work: Higher-order implicit strong numerical schemes for stochastic differential equations
cites work: Q4319807
cites work: Q4938228
cites work: Numerical Treatment of Stochastic Differential Equations
cites work: Stability Analysis of Numerical Schemes for Stochastic Differential Equations
cites work: Two-stage stochastic Runge-Kutta methods for stochastic differential equations
DOI: 10.1016/J.CAM.2007.11.001
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description: scientific article; zbMATH DE number 5368371