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Volume 22, Issue 4
The Homotopy Perturbation Method and the Adomian Decomposition Method for the Nonlinear Coupled Equations

Elsayed M. E. Zayed & H. M. Abdel Rahman

DOI: 10.4208/jpde.v22.n4.3

J. Part. Diff. Eq., 22 (2009), pp. 334-351.

Published online: 2009-11

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  • Abstract

In this paper, we have used the homotopy perturbation and the Adomian decomposition methods to study the nonlinear coupled Kortewge-de Vries and shallow water equations. The main objective of this paper is to propose alternative methods of solutions, which do not require small parameters and avoid linearization and physical unrealistic assumptions. The proposed methods give more general exact solutions without much extra effort and the results reveal that the homotopy perturbation and the Adomian decomposition methods are very effective, convenient and quite accurate to the systems of coupled nonlinear equations.

  • Keywords

Homotopy perturbation method Adomian decomposition method coupled Korteweg-de Vries equations shallow water equations

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COPYRIGHT: © Global Science Press

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@Article{JPDE-22-334, author = {Elsayed M. E. Zayed and H. M. Abdel Rahman }, title = {The Homotopy Perturbation Method and the Adomian Decomposition Method for the Nonlinear Coupled Equations}, journal = {Journal of Partial Differential Equations}, year = {2009}, volume = {22}, number = {4}, pages = {334--351}, abstract = {

In this paper, we have used the homotopy perturbation and the Adomian decomposition methods to study the nonlinear coupled Kortewge-de Vries and shallow water equations. The main objective of this paper is to propose alternative methods of solutions, which do not require small parameters and avoid linearization and physical unrealistic assumptions. The proposed methods give more general exact solutions without much extra effort and the results reveal that the homotopy perturbation and the Adomian decomposition methods are very effective, convenient and quite accurate to the systems of coupled nonlinear equations.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v22.n4.3}, url = {http://global-sci.org/intro/article_detail/jpde/5261.html} }
TY - JOUR T1 - The Homotopy Perturbation Method and the Adomian Decomposition Method for the Nonlinear Coupled Equations AU - Elsayed M. E. Zayed & H. M. Abdel Rahman JO - Journal of Partial Differential Equations VL - 4 SP - 334 EP - 351 PY - 2009 DA - 2009/11 SN - 22 DO - http://doi.org/10.4208/jpde.v22.n4.3 UR - https://global-sci.org/intro/article_detail/jpde/5261.html KW - Homotopy perturbation method KW - Adomian decomposition method KW - coupled Korteweg-de Vries equations KW - shallow water equations AB -

In this paper, we have used the homotopy perturbation and the Adomian decomposition methods to study the nonlinear coupled Kortewge-de Vries and shallow water equations. The main objective of this paper is to propose alternative methods of solutions, which do not require small parameters and avoid linearization and physical unrealistic assumptions. The proposed methods give more general exact solutions without much extra effort and the results reveal that the homotopy perturbation and the Adomian decomposition methods are very effective, convenient and quite accurate to the systems of coupled nonlinear equations.

Elsayed M. E. Zayed and H. M. Abdel Rahman . (2009). The Homotopy Perturbation Method and the Adomian Decomposition Method for the Nonlinear Coupled Equations. Journal of Partial Differential Equations. 22 (4). 334-351. doi:10.4208/jpde.v22.n4.3
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