Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations
We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/928765 |
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| _version_ | 1850163555825876992 |
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| author | Fukang Yin Junqiang Song Hongze Leng Fengshun Lu |
| author_facet | Fukang Yin Junqiang Song Hongze Leng Fengshun Lu |
| author_sort | Fukang Yin |
| collection | DOAJ |
| description | We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. |
| format | Article |
| id | doaj-art-e96adc012cb04fbca172a5690d0ffcf8 |
| institution | OA Journals |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-e96adc012cb04fbca172a5690d0ffcf82025-08-20T02:22:15ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/928765928765Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential EquationsFukang Yin0Junqiang Song1Hongze Leng2Fengshun Lu3College 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, ChinaChina Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, ChinaWe present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique.http://dx.doi.org/10.1155/2014/928765 |
| spellingShingle | Fukang Yin Junqiang Song Hongze Leng Fengshun Lu Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations The Scientific World Journal |
| title | Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations |
| title_full | Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations |
| title_fullStr | Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations |
| title_full_unstemmed | Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations |
| title_short | Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations |
| title_sort | couple of the variational iteration method and fractional order legendre functions method for fractional differential equations |
| url | http://dx.doi.org/10.1155/2014/928765 |
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