A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method

A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method

We propose a reproducing kernel method for solving the KdV equation with initial condition based on the reproducing kernel theory. The exact solution is represented in the form of series in the reproducing kernel Hilbert space. Some numerical examples have also been studied to demonstrate the accura...

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Bibliographic Details
Main Authors: Mustafa Inc, Ali Akgül, Adem Kiliçman
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/578942
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spelling doaj-250c3a912b3544a2a0e8914a204c309d2020-11-25T01:09:36ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/578942578942A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space MethodMustafa Inc0Ali Akgül1Adem Kiliçman2Department of Mathematics, Science Faculty, Firat University, 23119 Elaziğ, TurkeyDepartment of Mathematics, Education Faculty, Dicle University, 21280 Diyarbakır, TurkeyDepartment of Mathematics and Institute for Mathematical Research, University Putra Malaysia (UPM), Selangor, 43400 Serdang, MalaysiaWe propose a reproducing kernel method for solving the KdV equation with initial condition based on the reproducing kernel theory. The exact solution is represented in the form of series in the reproducing kernel Hilbert space. Some numerical examples have also been studied to demonstrate the accuracy of the present method. Results of numerical examples show that the presented method is effective.http://dx.doi.org/10.1155/2013/578942
collection DOAJ
language English
format Article
sources DOAJ
author Mustafa Inc
Ali Akgül
Adem Kiliçman
spellingShingle Mustafa Inc
Ali Akgül
Adem Kiliçman
A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method
Abstract and Applied Analysis
author_facet Mustafa Inc
Ali Akgül
Adem Kiliçman
author_sort Mustafa Inc
title A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method
title_short A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method
title_full A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method
title_fullStr A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method
title_full_unstemmed A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method
title_sort novel method for solving kdv equation based on reproducing kernel hilbert space method
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description We propose a reproducing kernel method for solving the KdV equation with initial condition based on the reproducing kernel theory. The exact solution is represented in the form of series in the reproducing kernel Hilbert space. Some numerical examples have also been studied to demonstrate the accuracy of the present method. Results of numerical examples show that the presented method is effective.
url http://dx.doi.org/10.1155/2013/578942
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AT aliakgul novelmethodforsolvingkdvequationbasedonreproducingkernelhilbertspacemethod
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