A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters-Reference-Cited by-同舟云学术

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

Published:2022-02-15 Issue: Volume:2022 Page:1-11
ISSN:1687-0425
Container-title:International Journal of Mathematics and Mathematical Sciences
language:en
Short-container-title:International Journal of Mathematics and Mathematical Sciences

Author:

Mekonnen Tariku Birabasa¹^ORCID,Duressa Gemechis File²^ORCID

Affiliation:

1. Department of Mathematics, Wollega University, Nekemte, Ethiopia

2. Department of Mathematics, Jimma University, Jimma, Ethiopia

Abstract

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.

Publisher

Hindawi Limited

Subject

Mathematics (miscellaneous)

Link

http://downloads.hindawi.com/journals/ijmms/2022/5410754.pdf

Reference28 articles.

1. A Numerical Method for Solving Boundary and Interior Layers Dominated Parabolic Problems with Discontinuous Convection Coefficient and Source Terms

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4. PARAMETER-UNIFORM FINITE ELEMENT METHOD FOR TWO-PARAMETER SINGULARLY PERTURBED PARABOLIC REACTION-DIFFUSION PROBLEMS

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