Work

Numerical solution of multi-dimensional time-fractional diffusion problems using an integral approach

Year: 2024

Type: article

Abstract: This paper presents a significant scheme to drive the numerical solution of multi-dimensional diffusion problems where the fractional derivatives are taken in Caputo sense. The Mohand homotopy integral transform scheme (MHITS) is the composition of Mohand integral transform (MIT) and the homotopy perturbation scheme (HPS) which can be used to investigate the numerical solution in the form of convergence series. This approach does not require any presumptions, limitations on elements, or any other hypothesis. The primary objective of this strategy is to perform its direct implementation to the recurrence relation. This method produces results in the form of a convergent series, which accurately predicts the exact results. Graphical results and plot error distribution show an excellent agreement between MHITS results and the exact solution.

Source: PLoS ONE

DOI: 10.1371/journal.pone.0304395

Authors: Muhammad Nadeem, Shamoona Jabeen, Fawziah M. Alotaibi, Yahya Alsayaad

Institutions: Qujing Normal University, University of Science and Technology Bannu, Taif University, Hodeidah University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,290

Funder: Taif University