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Research Article | Open Access

Fitted mesh methods based on non-polynomial splines for singularly perturbed boundary value problems with mixed shifts

T. Prathap, R. Nageshwar Rao( )
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, Tamil Nadu, India
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Abstract

In this paper, numerical schemes based on non-polynomial splines, namely, spline in compression, tension, and adaptive spline, are constructed for singularly perturbed boundary value problems with mixed shifts. A convergence analysis is carried out on the proposed methods. A comparitive study of the results is performed on test problems and presented in the form of tables. Graphs are drawn to illustrate the behavior of the solution to the problems.

Keywords

singular perturbationsdelaydifferential equationsnumerical methodsfitted meshsplines
CLC number: 65L10, 65L11, 65L12, 65L20, 65L50, 65L70

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AIMS Mathematics
Volume 9 Issue 10,
October 2024
Pages 26403-26434
DOI: 10.3934/math.20241285

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Cite this article:
Prathap T, Nageshwar Rao R. Fitted mesh methods based on non-polynomial splines for singularly perturbed boundary value problems with mixed shifts. AIMS Mathematics, 2024, 9(10): 26403-26434. https://doi.org/10.3934/math.20241285

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Received: 25 April 2024
Revised: 01 August 2024
Accepted: 07 August 2024
Published: 15 October 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)