Convergence and stability of numerical methods with variable step size for stochastic pantograph differential equations

DOI10.1080/00207160.2011.563843zbMath1261.65012OpenAlexW1978255949MaRDI QIDQ2885524

Yu Xiao, Haiying Zhang

Publication date: 23 May 2012

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

Full work available at URL: https://doi.org/10.1080/00207160.2011.563843

zbMATH Keywords

convergenceWiener processdelay equationbackward Euler methodvariable step sizemean-square stabilityunbounded memoryIto stochastic pantograph differential equations

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Ordinary differential equations and systems with randomness (34F05) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (10)

Convergence and stability of exponential integrators for semi-linear stochastic pantograph integro-differential equations with jump ⋮ Asymptotical mean-square stability of linearθ-methods for stochastic pantograph differential equations: variable stepsize and transformation approach ⋮ Stochastic \(\theta\)-methods for a class of jump-diffusion stochastic pantograph equations with random magnitude ⋮ Stability of numerical solutions for the stochastic pantograph differential equations with variable step size ⋮ The existence and asymptotic estimations of solutions to stochastic pantograph equations with diffusion and Lévy jumps ⋮ Collocation methods for nonlinear stochastic Volterra integral equations ⋮ Stability of numerical method for semi-linear stochastic pantograph differential equations ⋮ Approximate solutions of hybrid stochastic pantograph equations with Levy jumps ⋮ Stability with general decay rate of hybrid neutral stochastic pantograph differential equations driven by Lévy noise ⋮ Convergence and stability of split-step theta methods with variable step-size for stochastic pantograph differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation
• The \(\alpha \)th moment stability for the stochastic pantograph equation
• Existence and uniqueness of the solutions and convergence of semi-implicit Euler methods for stochastic pantograph equations
• Introduction to functional differential equations
• Asymptotic stability properties of \(\theta\)-methods for the pantograph equation
• Numerical investigation of the pantograph equation
• Razumikhin-type theorems on exponential stability of stochastic functional differential equations
• Moderate deviations for diffusions with Brownian potentials
• Introduction to the numerical analysis of stochastic delay differential equations
• On the \(\theta\)-method for delay differential equations with infinite lag
• An analysis of stability of Milstein method for stochastic differential equations with delay
• On the generalized pantograph functional-differential equation
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• Stability and Asymptotic Stability of Functional-Differential Equations

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