Linear multistep methods for the numerical solution of volterra functional differential equations†

DOI10.1080/00036817308839063zbMath0291.65020OpenAlexW2082689550WikidataQ58279931 ScholiaQ58279931MaRDI QIDQ4042624

Lucio Tavernini

Publication date: 1973

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036817308839063

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34Kxx)

Related Items (31)

On the asymptotic stability of \(\theta\)-methods for delay differential equations ⋮ Classical theory of Runge-Kutta methods for Volterra functional differential equations ⋮ Multistep numerical methods for functional differential equations ⋮ Solving linear Volterra integral equations with a piecewise linear maximum entropy method ⋮ A new class of one-step methods for the solution of Volterra functional differential equations ⋮ Converging multistep methods for initial value problems involving multivalued maps ⋮ A survey of recent advances in the numerical treatment of Volterra integral and integro-differential equations ⋮ Adams methods for neutral functional differential equations ⋮ A mathematical model of iron metabolism ⋮ A block-by-block method for the numerical solution of Volterra delay integro-differential equations ⋮ RUNGE–KUTTA METHODS FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS ⋮ The numerical solution of neutral functional differential equations by Adams predictor-corrector methods ⋮ Differential automata and their discrete simulators ⋮ Strong contractivity properties of numerical methods for ordinary and delay differential equations ⋮ Euler-Verfahren für neutrale Funktional-Differentialgleichungen ⋮ Sharpness results for state dependent delay differential equations: An overview ⋮ Convergence of a discretization method for integro-differential equations ⋮ On an initial-value method for quickly solving Volterra integral equations: A review ⋮ Convergence of multistep methods for Volterra functional differential equations ⋮ Online estimation and adaptive control for a class of history dependent functional differential equations ⋮ A note on solving Volterra integral equations with convolution kernels ⋮ The numerical treatment of Volterra integro-differential equations with unbounded delay ⋮ Asymptotic stability analysis of \(\theta\)-methods for functional differential equations ⋮ Linear multistep methods for a class of functional differential equations ⋮ The numerical solution of boundary value problems for second order functional differential equations by finite differences ⋮ Nonlinear Volterra integro-differential equations -- stability and numerical stability of \(\theta\)-methods ⋮ Round-off error for retarded ordinary differential equations: A priori bounds and estimates ⋮ One step methods for the numerical solution of volterra functional differential equations of neutral type ⋮ Numerical solutions of ordinary and retarded differential equations with discontinuous derivatives ⋮ Stability of Multistep Methods for Delay Differential Equations ⋮ Stability in linear multistep methods for pure delay equations

Cites Work

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• Existence and stability of solutions of a delay-differential system
• Linear Multistep Methods for Volterra Integro-Differential Equations
• One-Step Methods for the Numerical Solution of Volterra Functional Differential Equations

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