An efficient method for analyzing the solutions of the Korteweg-de Vries equation

Mohammed Al-Refai; Muhammed Syam

doi:10.1016/j.cnsns.2009.02.009

An efficient method for analyzing the solutions of the Korteweg-de Vries equation

Mohammed Al-Refai, Muhammed Syam

Department of Mathematical Sciences

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

3 Citations (Scopus)

Abstract

A new iterative method is applied to study the solutions of the Korteweg-de Vries (KdV) equation. The method is a modified form of the well known Adomian decomposition method (ADM), where it avoids the difficulty of computing the Adomian polynomials. We prove the existence of a unique solution of the KdV equation. And then, we show that the new method generates an infinite series which converges uniformly to the exact solution of the problem. Soliton solutions of the KdV equation are obtained by the new method. Numerical calculations indicate the effectiveness of the new method where the obtained results are very accurate and better than the ones obtained by the ADM.

Original language	English
Pages (from-to)	3825-3832
Number of pages	8
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	14
Issue number	11
DOIs	https://doi.org/10.1016/j.cnsns.2009.02.009
Publication status	Published - Nov 2009

Keywords

Iterative methods
Korteweg-de Vries equation
Partial differential equations

ASJC Scopus subject areas

Numerical Analysis
Modelling and Simulation
Applied Mathematics

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10.1016/j.cnsns.2009.02.009

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title = "An efficient method for analyzing the solutions of the Korteweg-de Vries equation",

abstract = "A new iterative method is applied to study the solutions of the Korteweg-de Vries (KdV) equation. The method is a modified form of the well known Adomian decomposition method (ADM), where it avoids the difficulty of computing the Adomian polynomials. We prove the existence of a unique solution of the KdV equation. And then, we show that the new method generates an infinite series which converges uniformly to the exact solution of the problem. Soliton solutions of the KdV equation are obtained by the new method. Numerical calculations indicate the effectiveness of the new method where the obtained results are very accurate and better than the ones obtained by the ADM.",

keywords = "Iterative methods, Korteweg-de Vries equation, Partial differential equations",

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T1 - An efficient method for analyzing the solutions of the Korteweg-de Vries equation

AU - Al-Refai, Mohammed

AU - Syam, Muhammed

PY - 2009/11

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N2 - A new iterative method is applied to study the solutions of the Korteweg-de Vries (KdV) equation. The method is a modified form of the well known Adomian decomposition method (ADM), where it avoids the difficulty of computing the Adomian polynomials. We prove the existence of a unique solution of the KdV equation. And then, we show that the new method generates an infinite series which converges uniformly to the exact solution of the problem. Soliton solutions of the KdV equation are obtained by the new method. Numerical calculations indicate the effectiveness of the new method where the obtained results are very accurate and better than the ones obtained by the ADM.

AB - A new iterative method is applied to study the solutions of the Korteweg-de Vries (KdV) equation. The method is a modified form of the well known Adomian decomposition method (ADM), where it avoids the difficulty of computing the Adomian polynomials. We prove the existence of a unique solution of the KdV equation. And then, we show that the new method generates an infinite series which converges uniformly to the exact solution of the problem. Soliton solutions of the KdV equation are obtained by the new method. Numerical calculations indicate the effectiveness of the new method where the obtained results are very accurate and better than the ones obtained by the ADM.

KW - Iterative methods

KW - Korteweg-de Vries equation

KW - Partial differential equations

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JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

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ER -

An efficient method for analyzing the solutions of the Korteweg-de Vries equation

Abstract

Keywords

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