Based on previous works, especially [1] and [2], we try in the present contribution to study some new aspects of the numerical solution of the KdV equation through the standard Adomian Decomposition Method. The use of the multistage Adomian Decomposition Method, applied to this equation, will be presented and discussed.
| Published in | Applied and Computational Mathematics (Volume 2, Issue 6) |
| DOI | 10.11648/j.acm.20130206.15 |
| Page(s) | 137-142 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2013. Published by Science Publishing Group |
KdV Equation - Standard and Multistage Adomian Decomposition Methods
| [1] | M.Akdi, M. B. Sedra, "Numerical KDV equation by the Adomian decomposition method", American Journal of Modern Physics. (2013) |
| [2] | M. Akdi, "Study of solitary waves: results of resolution by numerical methods of the Korteweg-de Vries equation and simulation of the fluid flow", Ph. D. Thesis. (2013) |
| [3] | M. Inc, On numerical solution of partial differential equation by the decomposition method, Kragujevac J Math. (2004) |
| [4] | García-Olivares, A., "Analytic solution of partial differential equations with Adomian's decomposition", Kybernetes (Bingley, U.K.: Emerald) 32: 354-368. (2003) |
| [5] | García-Olivares, A., "Analytical solution of nonlinear partial differential equations of physics", Kybernetes (Bingley, U.K.: Emerald) 32: 548-560. (2003) |
| [6] | Liao, S.J., "Homotopy Analysis Method in Nonlinear Differential Equation", Berlin & Beijing: Springer & Higher Education Press. (2012) |
| [7] | G. Adomian, "Solving Frontier Problems of Physics: The Decomposition Method", Kluwer, Dordrecht. (1994) |
| [8] | K. Abbaoui and Y. Cherruault, Convergence of adomian’s method applied to differential equations, Comp Math Appl. (1994) |
| [9] | K. Abbaoui and Y. Cherruault, Convergence of Adomian’s method applied to nonlinear equations, Math Computer Model. (1994) |
| [10] | N. Himoun, K. Abbaoui, and Y. Cherruault, New results of convergence of Adomian’s method,Kybernetes. (1999) |
| [11] | J. Biazar, E. Babolian, A. Nouri, R. Islam, "An alternate algorithm for computing Adomian decomposition method in special cases", Appl. Math. Comput. 138, 1–7. (2003) |
| [12] | J. Biazar, M. Tango, E. Babolian, R. Islam, "Solution of the kinetic modeling of lactic acid fermentation using Adomian decomposition method", Appl. Math. Comput. 139, 249–258. (2003) |
| [13] | Kolebaje O. T., Ojo O. L., Akinyemi P., Adenodi R. A., "On the application of the multistage laplace adomian decomposition method with pade approximation to the rabinovich-fabrikant system", Advances in Applied Science Research. (2013) |
| [14] | Nur Isnida Razali, M.S.H Chowdhury, Waqar Asrar, "The Multistage Adomian Decomposition Method for Solving Chaotic Lü System", Middle-East Journal of Scientific Research. (2013) |
APA Style
Mahmoud AKDI, Moulay Brahim SEDRA. (2013). Comments on the Adomian Decomposition Methods Applied to the KdV Equation. Applied and Computational Mathematics, 2(6), 137-142. https://doi.org/10.11648/j.acm.20130206.15
ACS Style
Mahmoud AKDI; Moulay Brahim SEDRA. Comments on the Adomian Decomposition Methods Applied to the KdV Equation. Appl. Comput. Math. 2013, 2(6), 137-142. doi: 10.11648/j.acm.20130206.15
AMA Style
Mahmoud AKDI, Moulay Brahim SEDRA. Comments on the Adomian Decomposition Methods Applied to the KdV Equation. Appl Comput Math. 2013;2(6):137-142. doi: 10.11648/j.acm.20130206.15
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.acm.20130206.15,
author = {Mahmoud AKDI and Moulay Brahim SEDRA},
title = {Comments on the Adomian Decomposition Methods Applied to the KdV Equation},
journal = {Applied and Computational Mathematics},
volume = {2},
number = {6},
pages = {137-142},
doi = {10.11648/j.acm.20130206.15},
url = {https://doi.org/10.11648/j.acm.20130206.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130206.15},
abstract = {Based on previous works, especially [1] and [2], we try in the present contribution to study some new aspects of the numerical solution of the KdV equation through the standard Adomian Decomposition Method. The use of the multistage Adomian Decomposition Method, applied to this equation, will be presented and discussed.},
year = {2013}
}
TY - JOUR T1 - Comments on the Adomian Decomposition Methods Applied to the KdV Equation AU - Mahmoud AKDI AU - Moulay Brahim SEDRA Y1 - 2013/11/20 PY - 2013 N1 - https://doi.org/10.11648/j.acm.20130206.15 DO - 10.11648/j.acm.20130206.15 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 137 EP - 142 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20130206.15 AB - Based on previous works, especially [1] and [2], we try in the present contribution to study some new aspects of the numerical solution of the KdV equation through the standard Adomian Decomposition Method. The use of the multistage Adomian Decomposition Method, applied to this equation, will be presented and discussed. VL - 2 IS - 6 ER -
Email: