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Journal of Applied Mathematics and Computing

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25-02-2021 | Original Research

A second order numerical method for singularly perturbed problem with non-local boundary condition

Authors: Musa Cakir, Gabil M. Amiraliyev

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2021

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Abstract

The aim of this paper is to present a monotone numerical method on uniform mesh for solving singularly perturbed three-point reaction–diffusion boundary value problems. Firstly, properties of the exact solution are analyzed. Difference schemes are established by the method of the integral identities with the appropriate quadrature rules with remainder terms in integral form. It is then proved that the method is second-order uniformly convergent with respect to singular perturbation parameter, in discrete maximum norm. Finally, one numerical example is presented to demonstrate the efficiency of the proposed method.

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Title: A second order numerical method for singularly perturbed problem with non-local boundary condition
Authors: Musa Cakir
Gabil M. Amiraliyev
Publication date: 25-02-2021
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2021
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-021-01506-z

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