Approximate Numerical solutions for the nonlinear dispersive shallow water waves as the Fornberg–Whitham model equations

•Applications of a new analyzing method: modified variational iteration algorithm-I.•Approximate numerical solution of nonlinear Fornberg-Whitham model equation.•Use of an auxiliary parameter for ensuring rapid convergence of the solution.•New methodology for obtaining the unknown auxiliary paramete...

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Bibliographic Details
Published in:Results in physics Vol. 22; p. 103907
Main Authors: Ahmad, Hijaz, Seadawy, Aly R., Ganie, Abdul Hamid, Rashid, Saima, Khan, Tufail A., Abu-Zinadah, Hanaa
Format: Journal Article
Language:English
Published: Elsevier B.V 01.03.2021
Elsevier
Subjects:
ADM
Fornberg–Whitham equation
HAM
Modified Fornberg–Whitham equation
MVIA-I
RKHSM
VIM
HAM
Fornberg–Whitham equation
Modified Fornberg–Whitham equation
ADM
VIM
MVIA-I
RKHSM
ISSN:2211-3797, 2211-3797
Online Access:Get full text
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Summary:•Applications of a new analyzing method: modified variational iteration algorithm-I.•Approximate numerical solution of nonlinear Fornberg-Whitham model equation.•Use of an auxiliary parameter for ensuring rapid convergence of the solution.•New methodology for obtaining the unknown auxiliary parameter.•Applications of modified variational iteration algorithm-I in various fields of physical sciences and engineering. The nonlinear partial differential equations having travelling or solitary wave solutions is numerically challenging, in which one of the important type is the Fornberg–Whitham model equation. This article aims to solve the Fornberg–Whitham type equations numerically via the variational iteration algorithm-I (MVIA-I). The MVIA-I gives approximate and exact solutions with easily computable terms to linear and nonlinear PDEs without the linearization or discretization, small perturbation and Adomian polynomials. To assess the precision, reliability and compactness of the recommended algorithm, we have compared the obtained results with the traditional variational iteration method (VIM), homotopy analysis method, reproducing kernel Hilbert space method and Adomian’s decomposition method which reveals that the MVIA-I is computationally attractive, exceptionally productive and is more reliable than the others techniques used in the literature.
ISSN:2211-3797
2211-3797
DOI:10.1016/j.rinp.2021.103907