A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems
Joint Authors
Bhrawy, Ali H.
Alghamdi, Mohammad Ali
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-08-27
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Bhrawy, Ali H.& Alghamdi, Mohammad Ali. 2013. A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-462078
Modern Language Association (MLA)
Bhrawy, Ali H.& Alghamdi, Mohammad Ali. A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems. Abstract and Applied Analysis No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-462078
American Medical Association (AMA)
Bhrawy, Ali H.& Alghamdi, Mohammad Ali. A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-462078
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-462078