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Numerical Solution of Second-Order Linear Delay Differential and Integro-Differential Equations by Using Taylor Collocation Method

A. Bellour

http://orcid.org/0000-0002-3644-0804

Laboratory of Applied Mathematics and Didactics, Ecole Normale Supérieure de Constantine, Constantine, Algeria

E-mail Address: bellourazze123@yahoo.com

Corresponding author.

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M. Bousselsal

Laboratoire d’analyse nonlineaire Vieux Kouba, 11 16050, Algiers, Algeria

E-mail Address: bousselsal55@gmail.com

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, and

H. Laib

Laboratoire d’analyse nonlineaire Vieux Kouba, 11 16050, Algiers, Algeria

E-mail Address: hafida.laib@gmail.com

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https://doi.org/10.1142/S0219876219500701Cited by:10 (Source: Crossref)

Abstract

The main purpose of this work is to provide a numerical approach for linear second-order differential and integro-differential equations with constant delay. An algorithm based on the use of Taylor polynomials is developed to construct a collocation solution $u \in S_{m}^{(1)} (Π_{N})$ $u \in S_{m}^{(1)} (Π_{N})$ for approximating the solution of second-order linear DDEs and DIDEs. It is shown that this algorithm is convergent. Some numerical examples are included to demonstrate the validity of this algorithm.

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