Stability of linear multistep methods for delay integro-differential equations

Authors:
Chengming Huang
Affiliations:
Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China
Venue:
Computers & Mathematics with Applications
Year:
2008

Citing 5
Cited 2

Stability properties of a scheme for the approximate solution of a delay-integro-differential equation

Selected papers from the international conference on Numerical solution of Volterra and delay equations
Stability of Runge-Kutta methods for delay integro-differential equations

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Stability of θ-methods for delay integro-differential equations

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An Analysis of Delay-Dependent Stability for Ordinary and Partial Differential Equations with Fixed and Distributed Delays

SIAM Journal on Scientific Computing
Stability analysis of Volterra delay-integro-differential equations and their backward differentiation time discretization

Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)

Asymptotic and numerical stability of systems of neutral differential equations with many delays

Journal of Computational and Applied Mathematics
Convergence and stability of extended block boundary value methods for Volterra delay integro-differential equations

Applied Numerical Mathematics

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Abstract

This paper is concerned with the numerical solution of delay integro-differential equations. The adaptation of linear multistep methods is considered. The emphasis is on the linear stability of numerical methods. It is shown that every A-stable, strongly 0-stable linear multistep method of Pouzet type can preserve the delay-independent stability of the underlying linear systems. In addition, some delay-dependent stability conditions for the stability of numerical methods are also given.