International Journal of Computing Science and Applied Mathematics
Vol 7, No 2 (2021)

Accelerated Numerical Method for Singularly Perturbed Differential Difference Equations

Habtamu Garoma Debela (Jimma University)
Gemechis File Duressa (Jimma University)
Masho Jima Kebeto (Jimma University)



Article Info

Publish Date
17 Aug 2021

Abstract

In this paper, accelerated finite difference method for solving singularly perturbed delay reaction-diffusion equations is presented. First, the solution domain is discretized. Then, the derivatives in the given boundary value problem are replaced by finite difference approximations and the numerical scheme that provides algebraic systems of equations is obtained, which can easily be solved by Thomas algorithm. The consistency, stability and convergence of the method have been established. To increase the accuracy of our established scheme we used Richardson's extrapolation techniques. To validate the applicability of the proposed method, four model examples have been considered and solved for different values of perturbation parameters and mesh sizes. The numerical results have been presented in tables and graphs to illustrate; the present method approximates the exact solution very well. Moreover, the present method gives better accuracy than the existing numerical methods mentioned in the literature.

Copyrights © 2021






Journal Info

Abbrev

ijcsam

Publisher

Subject

Computer Science & IT Education Mathematics

Description

(IJCSAM) International Journal of Computing Science and Applied Mathematics is an open access journal publishing advanced results in the fields of computations, science and applied mathematics, as mentioned explicitly in the scope of the journal. The journal is geared towards dissemination of ...