Blow-up solutions obtained using the decomposition method

Lesnic, D.

doi:10.1016/j.chaos.2005.08.003

Cited by 29 publications

(14 citation statements)

References 41 publications

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“…The Boussinesq equation is one of the model partial differential equation of the nonlinear dispersive waves, which has many application in many areas, e.g., ion-acoustic wave in plasma, magnetohydrordnamics wave in plasma, longitudinal dispersive wave in elastic rods, pressure wave in liquid-gas bubble mixtures, and rotating flow down a tube. Mathematical theory for the Boussinesq equation was developed in [3][4][5][6]. Various numerical techniques have been proposed to solve the Boussinesq equation.…”

Section: Introductionmentioning

confidence: 99%

Comparing numerical methods for Boussinesq equation model problem

Bulut

2008

Numerical Methods Partial

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This article applies three methods to solve a class of nonlinear differential equations. We obtain the exact solution and numerical solution of the Boussinesq equation for certain initial condition. Comparsion of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions. The numerical results demonstrate that those methods are quite accurate and readily implemented.

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Section: Introductionmentioning

confidence: 99%

Comparing numerical methods for Boussinesq equation model problem

Bulut

2008

Numerical Methods Partial

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“…Ref. [21] deals with obtaining explicit solutions of a generalized nonlinear Boussinesq equation using this method.…”

Section: A Adomian Decomposition Methodsmentioning

confidence: 99%

The numerical solution of the second Painlevé equation

Dehghan

Shakeri

2009

Numerical Methods Partial

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The Painlevé equations were discovered by Painlevé, Gambier and their colleagues during studying a nonlinear second-order ordinary differential equation. The six equations which bear Painlevé's name are irreducible in the sense that their general solutions cannot be expressed in terms of known functions. Painlevé has derived these equations on the sole requirement that their solutions should be free from movable singularities. Many situations in mathematical physics reduce ultimately to Painlevé equations: applications including statistical mechanics, plasma physics, nonlinear waves, quantum gravity, quantum field theory, general relativity, nonlinear optics, and fiber optics. This fact has caused a significant interest to the study of these equations in recent years. In this study, the solution of the second Painlevé equation is investigated by means of Adomian decomposition method, homotopy perturbation method, and Legendre tau method. Then a numerical evaluation and comparison with the results obtained by the method of continuous analytic continuation are included.

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“…The VIM is a powerful method that provides approximate solutions or even closed form analytical solutions of nonlinear evolution equations and has some advantages over the ADM [21,22]. The format of the paper follows very much that of reference [11] where the ADM instead of the VIM was investigated.…”

Section: Introductionmentioning

confidence: 98%

“…The approach of Kaptsov [7] and Andreev et al [8] introduced an efficient algorithm to handle the Boussinesq equation and developed multisolution solutions. The implementation of Adomian Decomposition Method (ADM) and its modified form to Boussinesq equation were introduced by Wazwaz [9], ElSayad et al [10] and Lesnic [11]. Abbasy [12] solved the Boussinesq equation by using ADM-Pade technique.…”

Section: Introductionmentioning

confidence: 99%