A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/306746 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |