Asymptotical stability of numerical methods with constant stepsize for pantograph equations

DOI10.1007/s10543-005-0022-3zbMath1095.65075OpenAlexW2053823159MaRDI QIDQ2490356

Yanyan Li

Publication date: 2 May 2006

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-005-0022-3

zbMATH Keywords

stabilitynumerical experimentsasymptotic stability\(\theta\)-methodspantograph equationDelay differential equations

Mathematics Subject Classification ID

Related Items (22)

Stochastic stability for pantograph multi-group models with dispersal and stochastic perturbation ⋮ Asymptotical mean-square stability of linearθ-methods for stochastic pantograph differential equations: variable stepsize and transformation approach ⋮ Classical theory of linear multistep methods for Volterra functional differential equations ⋮ Fast and precise spectral method for solving pantograph type Volterra integro-differential equations ⋮ Stability of collocation methods for delay differential equations with vanishing delays ⋮ Numerical solution of the delay differential equations of pantograph type via Chebyshev polynomials ⋮ Stability of the analytic and numerical solutions for impulsive differential equations ⋮ The existence and asymptotic estimations of solutions to stochastic pantograph equations with diffusion and Lévy jumps ⋮ A new collocation method for approximate solution of the pantograph functional differential equations with proportional delay ⋮ Asymptotic bounds for linear difference systems ⋮ Convergence and stability of a numerical method for nonlinear stochastic pantograph equations ⋮ A new computational approach for the solutions of generalized pantograph-delay differential equations ⋮ The global solutions and moment boundedness of stochastic multipantograph equations ⋮ The \(\alpha \)th moment stability for the stochastic pantograph equation ⋮ The existence of periodic solutions for coupled pantograph Rayleigh system ⋮ Recent advances in the numerical analysis of Volterra functional differential equations with variable delays ⋮ Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays ⋮ On collocation methods for delay differential and Volterra integral equations with proportional delay ⋮ Series solution for a delay differential equation arising in electrodynamics ⋮ Mean-square stability analysis for nonlinear stochastic pantograph equations by transformation approach ⋮ Stability with general decay rate of hybrid neutral stochastic pantograph differential equations driven by Lévy noise ⋮ Stability results for impulsive pantograph equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the discretization of differential and Volterra integral equations with variable delay
• Asymptotic stability analysis of \(\theta\)-methods for functional differential equations
• Stability of numerical methods for delay differential equations
• Introduction to functional differential equations
• Asymptotic stability properties of \(\theta\)-methods for the pantograph equation
• Exact and discretized stability of the pantograph equation
• Numerical investigation of the pantograph equation
• \(\mathcal H\)-stability of Runge-Kutta methods with general variable stepsize for pantograph equation.
• On the attainable order of collocation methods for delay differential equations with proportional delay
• Stability analysis of \(\theta\)-methods for neutral functional- differential equations
• On the \(\theta\)-method for delay differential equations with infinite lag
• Stability of difference Volterra equations: Direct Lyapunov method and numerical procedure
• Stability of Runge-Kutta methods for the generalized pantograph equation
• On the dynamics of a discretized neutral equation
• On the generalized pantograph functional-differential equation
• 13.—The Functional Differential Equation y′(x) = ay(λx) + by(x)
• On Nonlinear Delay Differential Equations
• Stability of one-leg  -methods for the variable coefficient pantograph equation on the quasi-geometric mesh
• Numerical Methods for Delay Differential Equations
• Stability of the Discretized Pantograph Differential Equation
• On a Functional Differential Equation

This page was built for publication: Asymptotical stability of numerical methods with constant stepsize for pantograph equations