\(H_{\alpha}\)-stability of modified Runge-Kutta methods for nonlinear neutral pantograph equations

DOI10.1016/j.jmaa.2007.02.035zbMath1125.65076OpenAlexW2066293965MaRDI QIDQ2642176

Yanyan Li

Publication date: 20 August 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.02.035

zbMATH Keywords

numerical experimentsGauss-Legendre methodsasymptotical stabilityalgebraic stabilitymodified Runge-Kutta methods\(H_{\alpha}\)-stabilitynonlinear neutral pantograph equationone-leg \(\theta\) methodsRadau IA, Radau IIA and Lobato IIIC methods

Mathematics Subject Classification ID

Related Items (11)

Solving generalized pantograph equations by shifted orthonormal Bernstein polynomials ⋮ High order stable Runge-Kutta methods for nonlinear generalized pantograph equations on the geometric mesh ⋮ Fully-geometric mesh one-leg methods for the generalized pantograph equation: approximating Lyapunov functional and asymptotic contractivity ⋮ An efficient IMEX method for nonlinear functional differential equations with state-dependent delay ⋮ Almost surely asymptotic stability of exact and numerical solutions for neutral stochastic pantograph equations ⋮ Razumikhin-type theorem and mean square asymptotic behavior of the backward Euler method for neutral stochastic pantograph equations ⋮ \(\varepsilon\)-approximate polynomial solutions for the multi-pantograph equation with variable coefficients ⋮ Optimal convergence orders of fully geometric mesh one-leg methods for neutral differential equations with vanishing variable delay ⋮ Preserving stability implicit Euler method for nonlinear Volterra and neutral functional differential equations in Banach space ⋮ Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays ⋮ Mean-square stability analysis for nonlinear stochastic pantograph equations by transformation approach

Cites Work

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• Nonlinear stability of Runge-Kutta methods applied to infinite-delay-differential equations
• On the \(\theta\)-method for delay differential equations with infinite lag
• Stability of one-leg  -methods for the variable coefficient pantograph equation on the quasi-geometric mesh
• Stability and Asymptotic Stability of Functional-Differential Equations
• The stability of modified Runge-Kutta methods for the pantograph equation
• On a Functional Differential Equation
• Discretized Stability and Error Growth of The Nonautonomous Pantograph Equation

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