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The optimal homotopy analysis method applied on nonlinear time‐fractional hyperbolic partial differential equation s
Author(s) -
Bahia Ghenaiet,
Ouannas Adel,
Batiha Iqbal M.,
Odibat Zaid
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22639
Subject(s) - mathematics , homotopy analysis method , hyperbolic partial differential equation , linearization , nonlinear system , partial differential equation , hyperbolic function , taylor series , convergence (economics) , series (stratigraphy) , homotopy , matlab , fractional calculus , partial derivative , numerical analysis , mathematical analysis , computer science , paleontology , physics , quantum mechanics , pure mathematics , economics , biology , economic growth , operating system
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.