Title: A uniformly convergent numerical method for singularly perturbed delay parabolic partial differential equation through non-polynomial spline technique

Authors: Awoke Andargie Tiruneh; Getachew Adamu Derese; Mulunesh Amsalu Ayele

Addresses: Department of Mathematics, College of Sciences, Bahir Dar University, Bahir Dar, 251, Ethiopia ' Department of Mathematics, College of Sciences, Bahir Dar University, Bahir Dar, 251, Ethiopia ' Department of Mathematics, College of Sciences, Bahir Dar University, Bahir Dar, 251, Ethiopia

Abstract: In this article, we proposed a uniformly convergent numerical method to solve singularly perturbed delay parabolic partial differential equation of convection-diffusion type. The scheme is developed using non-polynomial spline method by introducing a fitting factor in the spatial variable and Crank Nicholson finite difference method for time derivative. The stability and convergence analysis of the proposed method is made, it is found that this method is unconditionally stable and is convergent. Numerical investigations are carried out to demonstrate the efficacy and uniform convergence of the proposed scheme, and the obtained numerical results show that the results of the present method are more accurate than the results of some other methods discussed in the literature.

Keywords: singularly perturbation; time-delay parabolic; non-polynomial spline; boundary layer.

DOI: 10.1504/IJCSM.2023.135047

International Journal of Computing Science and Mathematics, 2023 Vol.18 No.4, pp.365 - 377

Received: 27 Dec 2021
Accepted: 14 Mar 2023
Published online: 28 Nov 2023 *

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