Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations
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 t...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/8630895 |
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| _version_ | 1832567371551735808 |
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| author | Qingxue Huang Fuqiang Zhao Jiaquan Xie Lifeng Ma Jianmei Wang Yugui Li |
| author_facet | Qingxue Huang Fuqiang Zhao Jiaquan Xie Lifeng Ma Jianmei Wang Yugui Li |
| author_sort | Qingxue Huang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-63b49d39d3cd4705b8af64ba5f1a3579 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-63b49d39d3cd4705b8af64ba5f1a35792025-02-03T01:01:33ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/86308958630895Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential EquationsQingxue Huang0Fuqiang Zhao1Jiaquan Xie2Lifeng Ma3Jianmei Wang4Yugui Li5College of Mechanical Engineering, Taiyuan University of Science & Technology, Taiyuan, Shanxi 030024, ChinaCollege of Mechanical Engineering, Taiyuan University of Science & Technology, Taiyuan, Shanxi 030024, ChinaCollege of Mechanical Engineering, Taiyuan University of Science & Technology, Taiyuan, Shanxi 030024, ChinaCollege of Mechanical Engineering, Taiyuan University of Science & Technology, Taiyuan, Shanxi 030024, ChinaCollege of Mechanical Engineering, Taiyuan University of Science & Technology, Taiyuan, Shanxi 030024, ChinaCollege of Mechanical Engineering, Taiyuan University of Science & Technology, Taiyuan, Shanxi 030024, ChinaIn 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.http://dx.doi.org/10.1155/2017/8630895 |
| spellingShingle | Qingxue Huang Fuqiang Zhao Jiaquan Xie Lifeng Ma Jianmei Wang Yugui Li Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations Discrete Dynamics in Nature and Society |
| title | Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations |
| title_full | Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations |
| title_fullStr | Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations |
| title_full_unstemmed | Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations |
| title_short | Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations |
| title_sort | numerical approach based on two dimensional fractional order legendre functions for solving fractional differential equations |
| url | http://dx.doi.org/10.1155/2017/8630895 |
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