Stability of the analytic and numerical solutions for impulsive differential equations

DOI10.1016/J.APNUM.2010.12.005zbMath1233.65044OpenAlexW2013150186MaRDI QIDQ643352

Hui Liang, Ming-Zhu Liu, Minghui Song

Publication date: 28 October 2011

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2010.12.005

zbMATH Keywords

impulsive differential equation\(\theta\)-methodsstability of analytic solutionstability of numerical method

Mathematics Subject Classification ID

Ordinary differential equations with impulses (34A37) Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical investigation of stability of solutions to ordinary differential equations (65L07)

Related Items (15)

Finite-Time Stability and Instability of Nonlinear Impulsive Systems ⋮ Numerical oscillation of neutral logistic delay differential equation ⋮ Convergence and stability of impulsive stochastic differential equations ⋮ Asymptotical stability of Runge-Kutta methods for nonlinear impulsive differential equations ⋮ Existence and exponential stability for impulsive neutral stochastic functional differential equations driven by fBm with noncompact semigroup via Mönch fixed point ⋮ Oscillation analysis of numerical solutions for nonlinear delay differential equations of hematopoiesis with unimodal production rate ⋮ Linear multistep methods for impulsive delay differential equations ⋮ Mean-square stability of analytic solution and Euler-Maruyama method for impulsive stochastic differential equations ⋮ Analytic and numerical exponential asymptotic stability of nonlinear impulsive differential equations ⋮ Collocation methods for impulsive differential equations ⋮ Convergence and stability of Euler method for impulsive stochastic delay differential equations ⋮ hp-Legendre–Gauss collocation method for impulsive differential equations ⋮ Analytic and numerical stability of delay differential equations with variable impulses ⋮ Asymptotical stability of numerical methods for semi-linear impulsive differential equations ⋮ Convergence, consistency and zero stability of impulsive one-step numerical methods

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• Perron's theorem for linear impulsive differential equations with distributed delay
• Analysis of a predator-prey model with Holling II functional response concerning impulsive control strategy
• Exponential stability of the solutions of the initial value problem for systems with an impulse effect

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