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

M. A. Mohamed | Zendy; M. Sh. Torky | Zendy

Open Access

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

Author(s) -

M. A. Mohamed,

M. Sh. Torky

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/192519

Subject(s) - legendre polynomials , mathematics , fractional calculus , legendre wavelet , galerkin method , nonlinear system , algebraic equation , partial differential equation , mathematical analysis , exact solutions in general relativity , partial derivative , derivative (finance) , wavelet , computer science , physics , wavelet transform , discrete wavelet transform , financial economics , economics , quantum mechanics , artificial intelligence

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

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