Analytic studies and numerical simulations of the generalized Boussinesq equation

Mohamed Ali Hajji; Kamel Al-Khaled

doi:10.1016/j.amc.2007.02.090

Analytic studies and numerical simulations of the generalized Boussinesq equation

Mohamed Ali Hajji, Kamel Al-Khaled

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

The modified Adomian decomposition method is used to solve the generalized Boussinesq equation. The equation commonly describes the propagation of small amplitude long waves in several physical contents. The analytic solution of the equation is obtained in the form of a convergent series with easily computable components. For comparison purposes, a numerical algorithm, based on Chebyshev polynomials, is developed and simulated. Numerical results show that the modified Adomian decomposition method proves to be more accurate and computationally more efficient than the Galerkin-Chebyshev method.

Original language	English
Pages (from-to)	320-333
Number of pages	14
Journal	Applied Mathematics and Computation
Volume	191
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2007.02.090
Publication status	Published - Aug 15 2007

Keywords

Boundary-value problems
Chebyshev polynomials
Decomposition method
Numerical simulations
Singularly perturbed Boussinesq equation
Solitary wave solutions

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2007.02.090

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title = "Analytic studies and numerical simulations of the generalized Boussinesq equation",

abstract = "The modified Adomian decomposition method is used to solve the generalized Boussinesq equation. The equation commonly describes the propagation of small amplitude long waves in several physical contents. The analytic solution of the equation is obtained in the form of a convergent series with easily computable components. For comparison purposes, a numerical algorithm, based on Chebyshev polynomials, is developed and simulated. Numerical results show that the modified Adomian decomposition method proves to be more accurate and computationally more efficient than the Galerkin-Chebyshev method.",

keywords = "Boundary-value problems, Chebyshev polynomials, Decomposition method, Numerical simulations, Singularly perturbed Boussinesq equation, Solitary wave solutions",

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N2 - The modified Adomian decomposition method is used to solve the generalized Boussinesq equation. The equation commonly describes the propagation of small amplitude long waves in several physical contents. The analytic solution of the equation is obtained in the form of a convergent series with easily computable components. For comparison purposes, a numerical algorithm, based on Chebyshev polynomials, is developed and simulated. Numerical results show that the modified Adomian decomposition method proves to be more accurate and computationally more efficient than the Galerkin-Chebyshev method.

AB - The modified Adomian decomposition method is used to solve the generalized Boussinesq equation. The equation commonly describes the propagation of small amplitude long waves in several physical contents. The analytic solution of the equation is obtained in the form of a convergent series with easily computable components. For comparison purposes, a numerical algorithm, based on Chebyshev polynomials, is developed and simulated. Numerical results show that the modified Adomian decomposition method proves to be more accurate and computationally more efficient than the Galerkin-Chebyshev method.

KW - Boundary-value problems

KW - Chebyshev polynomials

KW - Decomposition method

KW - Numerical simulations

KW - Singularly perturbed Boussinesq equation

KW - Solitary wave solutions

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Analytic studies and numerical simulations of the generalized Boussinesq equation

Abstract

Keywords

ASJC Scopus subject areas

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