The stability of modified Runge-Kutta methods for the pantograph equation

DOI10.1090/S0025-5718-06-01844-8zbMath1094.65075OpenAlexW2011335808MaRDI QIDQ5470049

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Publication date: 29 May 2006

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-06-01844-8

zbMATH Keywords

numerical examplesasymptotic stabilityRunge-Kutta methodGauss-Legendre methods\(\theta\)-methodspantograph equationLobatto III A and III B methods

Mathematics Subject Classification ID

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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (14)

High order stable Runge-Kutta methods for nonlinear generalized pantograph equations on the geometric mesh ⋮ Stochastic stability for pantograph multi-group models with dispersal and stochastic perturbation ⋮ \(H_{\alpha}\)-stability of modified Runge-Kutta methods for nonlinear neutral pantograph equations ⋮ Asymptotical mean-square stability of linearθ-methods for stochastic pantograph differential equations: variable stepsize and transformation approach ⋮ Optimal superconvergence results for Volterra functional integral equations with proportional vanishing delays ⋮ Numerical stability of higher-order derivative methods for the pantograph equation ⋮ Unnamed Item ⋮ Variational iteration method for solving the multi -- pantograph delay equation ⋮ Collocation methods for Volterra functional integral equations with non-vanishing delays ⋮ \(\varepsilon\)-approximate polynomial solutions for the multi-pantograph equation with variable coefficients ⋮ On the asymptotics of the trapezoidal rule for the pantograph equation ⋮ 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

Cites Work

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• Matrix Analysis
• On the generalized pantograph functional-differential equation
• 13.—The Functional Differential Equation y′(x) = ay(λx) + by(x)
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• Stability and Asymptotic Stability of Functional-Differential Equations
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• On a Functional Differential Equation

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