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Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations
Joint Authors
Huang, Qingxue
Li, Yugui
Zhao, Fuqiang
Xie, Jiaquan
Ma, Lifeng
Wang, Jianmei
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-01-23
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
In this paper, a robust, effective, and accurate numerical approach is proposed to obtain the numerical solution of fractional differential equations.
The principal characteristic of the approach is the new orthogonal functions based on shifted Legendre polynomials to the fractional calculus.
Also the fractional differential operational matrix is driven.
Then the matrix with the Tau method is utilized to transform this problem into a system of linear algebraic equations.
By solving the linear algebraic equations, the numerical solution is obtained.
The approach is tested via some examples.
It is shown that the FLF yields better results.
Finally, error analysis shows that the algorithm is convergent.
American Psychological Association (APA)
Huang, Qingxue& Zhao, Fuqiang& Xie, Jiaquan& Ma, Lifeng& Wang, Jianmei& Li, Yugui. 2017. Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations. Discrete Dynamics in Nature and Society،Vol. 2017, no. 2017, pp.1-12.
https://search.emarefa.net/detail/BIM-1151855
Modern Language Association (MLA)
Huang, Qingxue…[et al.]. Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations. Discrete Dynamics in Nature and Society No. 2017 (2017), pp.1-12.
https://search.emarefa.net/detail/BIM-1151855
American Medical Association (AMA)
Huang, Qingxue& Zhao, Fuqiang& Xie, Jiaquan& Ma, Lifeng& Wang, Jianmei& Li, Yugui. Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations. Discrete Dynamics in Nature and Society. 2017. Vol. 2017, no. 2017, pp.1-12.
https://search.emarefa.net/detail/BIM-1151855
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1151855