A Legendre tau-Spectral Method for Solving Time-Fractional Heat Equation with Nonlocal Conditions
Joint Authors
Bhrawy, Ali H.
Alghamdi, Mohammad Ali
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-06-25
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
We develop the tau-spectral method to solve the time-fractional heat equation (T-FHE) with nonlocal condition.
In order to achieve highly accurate solution of this problem, the operational matrix of fractional integration (described in the Riemann-Liouville sense) for shifted Legendre polynomials is investigated in conjunction with tau-spectral scheme and the Legendre operational polynomials are used as the base function.
The main advantage in using the presented scheme is that it converts the T-FHE with nonlocal condition to a system of algebraic equations that simplifies the problem.
For demonstrating the validity and applicability of the developed spectral scheme, two numerical examples are presented.
The logarithmic graphs of the maximum absolute errors is presented to achieve the exponential convergence of the proposed method.
Comparing between our spectral method and other methods ensures that our method is more accurate than those solved similar problem.
American Psychological Association (APA)
Bhrawy, Ali H.& Alghamdi, Mohammad Ali. 2014. A Legendre tau-Spectral Method for Solving Time-Fractional Heat Equation with Nonlocal Conditions. The Scientific World Journal،Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-1050697
Modern Language Association (MLA)
Bhrawy, Ali H.& Alghamdi, Mohammad Ali. A Legendre tau-Spectral Method for Solving Time-Fractional Heat Equation with Nonlocal Conditions. The Scientific World Journal No. 2014 (2014), pp.1-7.
https://search.emarefa.net/detail/BIM-1050697
American Medical Association (AMA)
Bhrawy, Ali H.& Alghamdi, Mohammad Ali. A Legendre tau-Spectral Method for Solving Time-Fractional Heat Equation with Nonlocal Conditions. The Scientific World Journal. 2014. Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-1050697
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1050697