Approximate analytic solution for the KdV and Burger equations with the homotopy analysis method
type: Item
instance of: scholarly article
title: Approximate analytic solution for the KdV and Burger equations with the homotopy analysis method
zbMATH Open document ID: 1267.35201
DOI: 10.1155/2012/878349
author: Mojtaba Nazari
author: Faisal Salah
author: Zainal Abdul Aziz
author: Merbakhsh Nilashi
published in: Journal of Applied Mathematics
publication date: 2013-06-03T00:00:00Z
review text: Summary: The homotopy analysis method (HAM) is applied to obtain the approximate analytic solution of the Korteweg-de Vries (KdV) and Burgers equations. The homotopy analysis method (HAM) is an analytic technique which provides us with a new way to obtain series solutions of such nonlinear problems. HAM contains the auxiliary parameter \(\hbar\), which provides us with a straightforward way to adjust and control the convergence region of the series solution. The resulted HAM solution at 8th-order and 14th-order approximation is then compared with that of the exact soliton solutions of KdV and Burgers equations, respectively, and shown to be in excellent agreement.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35C10
Mathematics Subject Classification ID: 35C08
zbMATH DE Number: 6170003
Wikidata QID: Q58907535
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/878349
OpenAlex ID: W2039842545
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description: scientific article; zbMATH DE number 6170003