A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters

A numerical treatment via a difference scheme constructed by the Crank–Nicolson scheme for the time derivative and cubic spline in tension for the spatial derivatives on a layer resolving nonuniform Bakhvalov-type mesh for a singularly perturbed unsteady-state initial-boundary-value problem with two...

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Main Authors: Tariku Birabasa Mekonnen, Gemechis File Duressa
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2022/5410754
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author Tariku Birabasa Mekonnen
Gemechis File Duressa
author_facet Tariku Birabasa Mekonnen
Gemechis File Duressa
author_sort Tariku Birabasa Mekonnen
collection DOAJ
description A numerical treatment via a difference scheme constructed by the Crank–Nicolson scheme for the time derivative and cubic spline in tension for the spatial derivatives on a layer resolving nonuniform Bakhvalov-type mesh for a singularly perturbed unsteady-state initial-boundary-value problem with two small parameters is presented. Error analysis of the constructed scheme is discussed and shown to be parameter-uniformly convergent with second-order convergence. Numerical experimentation is taken to confirm the theoretical findings.
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institution Kabale University
issn 1687-0425
language English
publishDate 2022-01-01
publisher Wiley
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-6000ca422d5f45c9bbd4e64338ccaa6e2025-08-20T03:34:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252022-01-01202210.1155/2022/5410754A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two ParametersTariku Birabasa Mekonnen0Gemechis File Duressa1Department of MathematicsDepartment of MathematicsA numerical treatment via a difference scheme constructed by the Crank–Nicolson scheme for the time derivative and cubic spline in tension for the spatial derivatives on a layer resolving nonuniform Bakhvalov-type mesh for a singularly perturbed unsteady-state initial-boundary-value problem with two small parameters is presented. Error analysis of the constructed scheme is discussed and shown to be parameter-uniformly convergent with second-order convergence. Numerical experimentation is taken to confirm the theoretical findings.http://dx.doi.org/10.1155/2022/5410754
spellingShingle Tariku Birabasa Mekonnen
Gemechis File Duressa
A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters
International Journal of Mathematics and Mathematical Sciences
title A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters
title_full A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters
title_fullStr A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters
title_full_unstemmed A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters
title_short A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters
title_sort fitted mesh cubic spline in tension method for singularly perturbed problems with two parameters
url http://dx.doi.org/10.1155/2022/5410754
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AT gemechisfileduressa afittedmeshcubicsplineintensionmethodforsingularlyperturbedproblemswithtwoparameters
AT tarikubirabasamekonnen fittedmeshcubicsplineintensionmethodforsingularlyperturbedproblemswithtwoparameters
AT gemechisfileduressa fittedmeshcubicsplineintensionmethodforsingularlyperturbedproblemswithtwoparameters