A parameter-uniform finite difference scheme for singularly perturbed parabolic problem with two small parameters

Authors

  • Tesfaye Aga Bullo Department of Mathematics, Jimma University, Jimma, P. O. Box 378, Ethiopia https://orcid.org/0000-0001-6766-4803
  • Guy Aymard Degla Institut De Mathematiques et de sciences physiques, Universit D’Abomey Calavi, Benin
  • Gemechis File Duressa Department of Mathematics, Jimma University, Jimma, P. O. Box 378, Ethiopia

DOI:

https://doi.org/10.13052/ejcm2642-2085.30233

Keywords:

Parameter-uniform, singularly perturbed, parabolic problems, two-parameters, finite difference scheme, error bounds, and accurate solution.

Abstract

A parameter-uniform finite difference scheme is constructed and analyzed for solving singularly perturbed parabolic problems with two parameters. The solution involves boundary layers at both the left and right ends of the solution domain. A numerical algorithm is formulated based on uniform mesh finite difference approximation for time variable and appropriate piecewise uniform mesh for the spatial variable. Parameter-uniform error bounds are established for both theoretical and experimental results and observed that the scheme is second-order convergent. Furthermore, the present method produces a more accurate solution than some methods existing in the literature.   

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Author Biographies

Tesfaye Aga Bullo, Department of Mathematics, Jimma University, Jimma, P. O. Box 378, Ethiopia

Tesfaya Aga Bullo received B.Sc. degree from Addis Ababa University, M.Sc. from Bahr Dar University, and Ph.D. degree of Mathematics in Numerical Analysis from Jimma University, Ethiopia. Currently, he is an assistant professor of Mathematics at Jimma University, Ethiopia. His research interests are computational mathematics, numerical solution of singularly perturbed boundary value problems. He has published more than 25 research articles in reputable journals.

Guy Aymard Degla, Institut De Mathematiques et de sciences physiques, Universit D’Abomey Calavi, Benin

Guy Aymard Degla is a senor Mathematics professor in the Institute De Mathematiques et de sciences physiques, (IMSP), Universit D’Abomey Calavi, Benin.

Gemechis File Duressa, Department of Mathematics, Jimma University, Jimma, P. O. Box 378, Ethiopia

Gemechis File Duressa received his M.Sc. degree from Addis Ababa University, Ethiopia and Ph.D. degree from National Institute of Technology, Warangal, India. He is currently working as a full professor of Mathematics at Jimma University. His research interests include Numerical Methods for Singularly Perturbed Differential Equations (both ODE and PDE). As far as this, he has published more than 90 research articles in reputable journals.

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Published

2021-10-09

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Section

Original Article