New strategy for the numerical solution of multi-dimensional diffusion equations

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.

Solutions of a three-dimensional multi-term fractional anomalous solute transport model for contamination in groundwater

“…In this case, the following matrix expression of Eq (10) is obtained by employed the inverse multiquadric (IMQ) RBF cðk r hk À r p kÞ ¼ 1=…”

“…Fractional differential equations (FDEs) represent a broader category of conventional differential equations, accommodating derivatives of real or complex orders. These equations find extensive application in various areas, such as fluid mechanics, heat transfer, and electromagnetism [9][10][11]. Fractional partial differential equations (FPDEs), specifically, offer distinct advantages by providing a more accurate depiction of real-world phenomena that conventional DEs cannot adequately capture.…”

Dynamical analysis of a rotating rigid body containing a viscous incompressible fluid

“…The asymptotic solutions to this problem were obtained using a modification of the averaging approach (Volosov and Morgunov, 1971; Akulenko, 2002), in which some limited cases were examined (Akulenko et al , 2011). A porous medium using fractal theory (He and Liu, 2022; Eldesoky et al , 2020) and the stability of free gyrostat (Galal, 2022) might be extended to the present problem; furthermore, some perturbation techniques (He et al , 2022a; He and El-Dib, 2022; He et al , 2022b; Moatimid and Amer, 2022; Nadeem, 2022) are needed to study the complex problem.…”