Mean-square stability of semi-implicit Euler method for nonlinear neutral stochastic delay differential equations

• Published in: Applied numerical mathematics Vol. 61; no. 5; pp. 696 - 701
• Main Authors: Wang, Wenqiang, Chen, Yanping
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01.05.2011; Elsevier
• Subjects: Delay; Differential equations; Exact sciences and technology; Mathematical analysis; Mathematical models; Mathematics; Mean-square stability; Neutral stochastic delay differential equations; Nonlinearity; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Numerical stability; Sciences and techniques of general use; Semi-implicit Euler method; Sequences, series, summability; Stability; Stochasticity; Semi-implicit Euler method; Neutral stochastic delay differential equations; Mean-square stability; Differential equation; Stochastic method; Euler scheme; Non linear stability; Non linear equation; Numerical analysis; Neutral equation; Applied mathematics; Integral equation; Numerical stability; Stochastic equation
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2011.01.003

There are few results on the numerical stability of nonlinear neutral stochastic delay differential equations (NSDDEs). The aim of this paper is to establish some new results on the numerical stability for nonlinear NSDDEs. It is proved that the semi-implicit Euler method is mean-square stable under suitable condition. The theoretical result is also confirmed by a numerical experiment.