The optimal homotopy analysis method applied on nonlinear time‐fractional hyperbolic partial differential equations. Issue 3 (9th November 2020)

• Record Type: Journal Article
• Authors: Bahia, Ghenaiet; Ouannas, Adel; Batiha, Iqbal M.; Odibat, Zaid
• Is Part Of: Numerical methods for partial differential equations. Volume 37:Issue 3(2021)
• Page Start: 2008
• Page End: 2022
• Publication Date: 2020-11-09
• Subjects: Caputo fractional derivative -- homotopy analysis method -- linearization‐based approach of homotopy analysis method -- Taylor series -- time‐fractional hyperbolic PDEs; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22639
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: In this article, the most recent version of an optimal homotopy analysis method (HAM), called linearization‐based approach of HAM or simply LHAM, has been applied to obtain a numerical solution of one of the principal nonlinear fractional‐order hyperbolic problems known as the time‐fractional hyperbolic partial differential equation. Such method is constructed based on employing Taylor series linearization method in order to design an optimal auxiliary linear operator with its corresponding optimal initial guessing. These two optimum contributors will accelerate the convergence of series solutions for the problem at hand. Several numerical comparisons have revealed the efficiency of the proposed method in obtaining a numerical solution of the problem rather than that solution presented by using the standard HAM. All theoretical findings in this work have been verified numerically using MATLAB software package.