Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method

Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method

The Legendre multiwavelet Galerkin method is adopted to give the approximate solution for the nonlinear fractional partial differential equations (NFPDEs). The Legendre multiwavelet properties are presented. The main characteristic of this approach is using these properties together with the Galerki...

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Main Authors: M. A. Mohamed, M. Sh. Torky
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/192519
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spelling doaj-996e752267be4fb3968f1959cc14171c2020-11-24T23:08:41ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/192519192519Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin MethodM. A. Mohamed0M. Sh. Torky1Faculty of Science, Suez Canal University Ismailia, Ismailia, EgyptThe High Institute of Administration and Computer, Port Said University, Port Said, EgyptThe Legendre multiwavelet Galerkin method is adopted to give the approximate solution for the nonlinear fractional partial differential equations (NFPDEs). The Legendre multiwavelet properties are presented. The main characteristic of this approach is using these properties together with the Galerkin method to reduce the NFPDEs to the solution of nonlinear system of algebraic equations. We presented the numerical results and a comparison with the exact solution in the cases when we have an exact solution to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense.http://dx.doi.org/10.1155/2014/192519
collection DOAJ
language English
format Article
sources DOAJ
author M. A. Mohamed
M. Sh. Torky
spellingShingle M. A. Mohamed
M. Sh. Torky
Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method
Journal of Applied Mathematics
author_facet M. A. Mohamed
M. Sh. Torky
author_sort M. A. Mohamed
title Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method
title_short Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method
title_full Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method
title_fullStr Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method
title_full_unstemmed Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method
title_sort approximate solution of fractional nonlinear partial differential equations by the legendre multiwavelet galerkin method
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description The Legendre multiwavelet Galerkin method is adopted to give the approximate solution for the nonlinear fractional partial differential equations (NFPDEs). The Legendre multiwavelet properties are presented. The main characteristic of this approach is using these properties together with the Galerkin method to reduce the NFPDEs to the solution of nonlinear system of algebraic equations. We presented the numerical results and a comparison with the exact solution in the cases when we have an exact solution to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense.
url http://dx.doi.org/10.1155/2014/192519
work_keys_str_mv AT mamohamed approximatesolutionoffractionalnonlinearpartialdifferentialequationsbythelegendremultiwaveletgalerkinmethod
AT mshtorky approximatesolutionoffractionalnonlinearpartialdifferentialequationsbythelegendremultiwaveletgalerkinmethod
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