Open Access

ARTICLE

A Computational Analysis to Burgers Huxley Equation

by Muhammad Saqib¹, Muhammad Shoaib Arif^2,*, Shahid Hasnain³, Daoud S. Mashat⁴

1 Department of Mathematics, Numl University, Islamabad, 44000, Pakistan
2 Department of Mathematics, Air University, Islamabad, 44000, Pakistan
3 Department of Mathematics, Air University, Multan Campus, Multan, 66000, Pakistan
4 Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

* Corresponding Author: Muhammad Shoaib Arif. Email:

Computers, Materials & Continua 2021, 67(2), 2161-2183. https://doi.org/10.32604/cmc.2021.014507

Received 24 September 2020; Accepted 04 December 2020; Issue published 05 February 2021

Abstract

The efficiency of solving computationally partial differential equations can be profoundly highlighted by the creation of precise, higher-order compact numerical scheme that results in truly outstanding accuracy at a given cost. The objective of this article is to develop a highly accurate novel algorithm for two dimensional non-linear Burgers Huxley (BH) equations. The proposed compact numerical scheme is found to be free of superiors approximate oscillations across discontinuities, and in a smooth flow region, it efficiently obtained a high-order accuracy. In particular, two classes of higher-order compact finite difference schemes are taken into account and compared based on their computational economy. The stability and accuracy show that the schemes are unconditionally stable and accurate up to a two-order in time and to six-order in space. Moreover, algorithms and data tables illustrate the scheme efficiency and decisiveness for solving such non-linear coupled system. Efficiency is scaled in terms of L₂ and L_∞ norms, which validate the approximated results with the corresponding analytical solution. The investigation of the stability requirements of the implicit method applied in the algorithm was carried out. Reasonable agreement was constructed under indistinguishable computational conditions. The proposed methods can be implemented for real-world problems, originating in engineering and science.

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