Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions
A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs). The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs). The op...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/562140 |
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| _version_ | 1832564452355997696 |
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| author | Fukang Yin Junqiang Song Yongwen Wu Lilun Zhang |
| author_facet | Fukang Yin Junqiang Song Yongwen Wu Lilun Zhang |
| author_sort | Fukang Yin |
| collection | DOAJ |
| description | A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs). The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs). The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method. |
| format | Article |
| id | doaj-art-1a3e9c49eb1c42769e97de0ed466be4f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1a3e9c49eb1c42769e97de0ed466be4f2025-02-03T01:10:56ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/562140562140Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre FunctionsFukang Yin0Junqiang Song1Yongwen Wu2Lilun Zhang3College of Computer, National University of Defense Technology, Changsha 410073, ChinaCollege of Computer, National University of Defense Technology, Changsha 410073, ChinaCollege of Computer, National University of Defense Technology, Changsha 410073, ChinaCollege of Computer, National University of Defense Technology, Changsha 410073, ChinaA numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs). The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs). The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.http://dx.doi.org/10.1155/2013/562140 |
| spellingShingle | Fukang Yin Junqiang Song Yongwen Wu Lilun Zhang Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions Abstract and Applied Analysis |
| title | Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions |
| title_full | Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions |
| title_fullStr | Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions |
| title_full_unstemmed | Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions |
| title_short | Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions |
| title_sort | numerical solution of the fractional partial differential equations by the two dimensional fractional order legendre functions |
| url | http://dx.doi.org/10.1155/2013/562140 |
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