The improved stability analysis of the backward Euler method for neutral stochastic delay differential equations

DOI10.1080/00207160.2012.756479zbMath1277.60115OpenAlexW2062872373MaRDI QIDQ2855769

Zhanhua Yu

Publication date: 22 October 2013

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2012.756479

zbMATH Keywords

numerical solutionbackward Euler methodalmost sure exponential stabilitymean square exponential stabilityneutral stochastic delay differential equations

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items

Implicit numerical methods for highly nonlinear neutral stochastic differential equations with time-dependent delay ⋮ Asymptotic exponential stability of modified truncated EM method for neutral stochastic differential delay equations ⋮ Delay-derivative-dependent stability for neutral systems with time-varying delay and nonlinearity ⋮ Existence, uniqueness and almost surely asymptotic estimations of the solutions to neutral stochastic functional differential equations driven by pure jumps ⋮ Stability analysis of stochastic delay differential equations with Markovian switching driven by Lévy noise ⋮ Almost sure and mean square exponential stability of numerical solutions for neutral stochastic functional differential equations

Cites Work

• Mean-square stability of semi-implicit Euler method for nonlinear neutral stochastic delay differential equations
• Almost surely asymptotic stability of exact and numerical solutions for neutral stochastic pantograph equations
• Almost surely asymptotic stability of numerical solutions for neutral stochastic delay differential equations
• Almost sure exponential stability of numerical solutions for stochastic delay differential equations
• Almost sure asymptotic stability of drift-implicit \(\theta\)-methods for bilinear ordinary stochastic differential equations in \(\mathbb R^1\)
• Almost sure exponential stability of numerical solutions for stochastic delay differential equations with jumps
• Asymptotic properties of neutral stochastic differential delay equations

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