New strategy for the numerical solution of multi-dimensional diffusion equations
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 22 December 2022
Issue publication date: 25 April 2023
Abstract
Purpose
The purpose of this paper is to introduce an innovative strategy for the approximate solution of the heat flow problems in two- and three-dimensional spaces. This new strategy is very easy to implement and handles the restrictive variable that may ruin the physical nature of the problem.
Design/methodology/approach
This study combines Sawi transform (ST) and the homotopy perturbation method (HPM) to formulate the idea of Sawi homotopy perturbation transform method (SHPTM). First, this study implements ST to handle the recurrence relation and then incorporates HPM to derive the series solutions of this recurrence relation. ST has the advantage in that it does not require any assumptions or hypothesis for the evaluation of series solutions.
Findings
This strategy finds the results very accurate and close to the precise solution. The graphical observations and the surface solution demonstrate that SHPTM is a reliable and powerful scheme for finding the approximate solution of heat flow problems.
Originality/value
The study presents an original work. This study develops SHPTM for the approximate solution of two- and three-dimensional heat flow problems. The obtained results and graphical representation demonstrate that SHPTM is a very authentic and reliable approach.
Keywords
Citation
Nadeem, M. (2023), "New strategy for the numerical solution of multi-dimensional diffusion equations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 5, pp. 1939-1954. https://doi.org/10.1108/HFF-09-2022-0554
Publisher
:Emerald Publishing Limited
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