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, issue 1

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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https://doi.org/10.1155/2013/306746

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:306746

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