Convergence of Runge-Kutta methods for neutral Volterra delay-integro-differential equations

DOI10.1007/S11464-009-0021-9zbMath1396.65166OpenAlexW2099360046MaRDI QIDQ1022535

Wan-Sheng Wang, Shou-fu Li

Publication date: 22 June 2009

Published in: Frontiers of Mathematics in China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11464-009-0021-9

zbMATH Keywords

convergenceneutral differential equationRunge-Kutta methodVolterra delay-integro-differential equation

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (14)

A Legendre–Petrov–Galerkin method for solving Volterra integro-differential equations with proportional delays ⋮ Legendre spectral collocation methods for Volterra delay-integro-differential equations ⋮ A spectral method for a weakly singular Volterra integro-differential equation with pantograph delay ⋮ Fast and precise spectral method for solving pantograph type Volterra integro-differential equations ⋮ Legendre spectral collocation methods for pantograph Volterra delay-integro-differential equations ⋮ Nonlinear stability of one-leg methods for neutral Volterra delay-integro-differential equations ⋮ Convergence of Runge-Kutta methods for neutral delay integro-differential equations ⋮ Convergence of one-leg methods for neutral delay integro-differential equations ⋮ Superconvergent interpolants for collocation methods applied to Volterra integro-differential equations with delay ⋮ An \(hp\)-version of the \(C^0\)-continuous Petrov-Galerkin method for second-order Volterra integro-differential equations ⋮ Sinc numerical solution for pantograph Volterra delay-integro-differential equation ⋮ An \(h\)-\(p\) version of the Chebyshev spectral collocation method for Volterra integro-differential equations with vanishing delays ⋮ Stability analysis of implicit-explicit \(\theta\)-methods for composite stiff neutral functional differential equations in Banach space ⋮ The operational matrix of Chebyshev polynomials for solving pantograph-type Volterra integro-differential equations

Uses Software

• RODAS

Cites Work

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• Convergence of one-leg methods for nonlinear neutral delay integro-differential equations
• Natural continuous extension of Runge-Kutta methods for Volterra integrodiffential equations
• Stability properties of a scheme for the approximate solution of a delay- integro-differential equation
• Stability and error analysis of one-leg methods for nonlinear delay differential equations
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• \(B\)-theory of general linear methods for Volterra functional differential equations
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• Quasilinear Multistep Methods and Variable Step Predictor–Corrector Methods for Neutral Functional-Differential Equations
• Non-linear stability of a general class of differential equation methods
• Stability analysis of Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations
• Collocation Methods for Volterra Integral and Related Functional Differential Equations

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