T-stability of the semi-implicit Euler method for delay differential equations with multiplicative noise
type: Item
instance of: scholarly article
title: T-stability of the semi-implicit Euler method for delay differential equations with multiplicative noise
zbMATH Open document ID: 1195.65007
published in: Applied Mathematics and Computation
publication date: 2010-05-11T00:00:00Z
review text: The notion of T-stability concerns the behaviour of numerical methods (equipped with a driving process to be specified) when applied to the integration of stochastic ordinary differential equations. This concept can be easily extended, of course, to stochastic differential equations with delay. In essence, the numerical scheme is said to be T-stable if the solution it provides on a test linear equation tends to zero with probability one as time integration goes on. The author analyzes the T-stability of the semi-implicit Euler scheme applied to a linear delay differential equation with multiplicative noise (described by a standard Wiener process), giving conditions on the parameters of the method (the weight and step size) that guarantee this T-convergence. Now the Wiener process is approximated by a discrete random variable with two-point distribution (each with probability \(1/2\)). The numerical examples collected in the paper illustrate the obtained theoretical bounds for T-stability, and show that these are not optimal.
reviewed by: Fernando Casas
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 65L03
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 34K50
zbMATH DE Number: 5707080
zbMATH Keywords: delay differential equations
zbMATH Keywords: multiplicative noise
zbMATH Keywords: T-stability
zbMATH Keywords: semi-implicit Euler method
zbMATH Keywords: two-point random variable
zbMATH Keywords: stochastic ordinary differential equations
zbMATH Keywords: T-convergence
zbMATH Keywords: Wiener process
zbMATH Keywords: numerical examples
author: Wanrong Cao
MaRDI profile type: Publication
full work available at URL: j.amc.2010.01.118
OpenAlex ID: W1973659587
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DOI: 10.1016/J.AMC.2010.01.118
description: scientific article; zbMATH DE number 5707080