Stability of a class of Runge--Kutta methods for a family of pantograph equations of neutral type

DOI10.1016/j.amc.2006.01.084zbMath1168.65371OpenAlexW1983895661MaRDI QIDQ856108

N. E. Zubov

Publication date: 7 December 2006

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2006.01.084

zbMATH Keywords

numerical experimentsasymptotic stabilityRunge-Kutta methodsGauss-Legendre methodspantograph equationsRadau IIA methodsLobatto IIIC methodsneutral infinite delay-differential equationsRadau IA methods

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) 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 ⋮ An approximate solution for a neutral functional-differential equation with proportional delays ⋮ Fully-geometric mesh one-leg methods for the generalized pantograph equation: approximating Lyapunov functional and asymptotic contractivity ⋮ A new numerical method to solve pantograph delay differential equations with convergence analysis ⋮ Modified Chebyshev collocation method for pantograph-type differential equations ⋮ An efficient IMEX method for nonlinear functional differential equations with state-dependent delay ⋮ A Legendre-Gauss collocation method for neutral functional-differential equations with proportional delays ⋮ Numerical solution of the delay differential equations of pantograph type via Chebyshev polynomials ⋮ A new collocation method for approximate solution of the pantograph functional differential equations with proportional delay ⋮ Optimal convergence orders of fully geometric mesh one-leg methods for neutral differential equations with vanishing variable delay ⋮ Numerical solution of a class of functional-differential equations using Jacobi pseudospectral method ⋮ Application of natural transform method to fractional pantograph delay differential equations ⋮ Series solution for a delay differential equation arising in electrodynamics ⋮ Stability analysis of block boundary value methods for neutral pantograph equation

Cites Work

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• On neutral functional-differential equations with proportional delays
• Strong contractivity properties of numerical methods for ordinary and delay 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.
• Stability analysis of \(\theta\)-methods for neutral functional- differential equations
• On the \(\theta\)-method for delay differential equations with infinite lag
• Stability of Runge-Kutta methods for the generalized pantograph equation
• Matrix Analysis
• On the generalized pantograph functional-differential equation

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