A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems

A. H. Bhrawy and M. A. Alghamdi

Abstract and Applied Analysis, 2013, vol. 2013, 1-10

Abstract:

We extend the application of the Galerkin method for treating the multiterm fractional differential equations (FDEs) subject to initial conditions. A new shifted Legendre-Galerkin basis is constructed which satisfies exactly the homogeneous initial conditions by expanding the unknown variable using a new polynomial basis of functions which is built upon the shifted Legendre polynomials. A new spectral collocation approximation based on the Gauss-Lobatto quadrature nodes of shifted Legendre polynomials is investigated for solving the nonlinear multiterm FDEs. The main advantage of this approximation is that the solution is expanding by a truncated series of Legendre-Galerkin basis functions. Illustrative examples are presented to ensure the high accuracy and effectiveness of the proposed algorithms are discussed.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:306746

DOI: 10.1155/2013/306746

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