Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations
This paper develops a modified variational iteration method coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs). The approximate solutions of PDEs are calculated in the form of a series whose components are com...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/157956 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832562809123110912 |
|---|---|
| author | Fukang Yin Junqiang Song Xiaoqun Cao Fengshun Lu |
| author_facet | Fukang Yin Junqiang Song Xiaoqun Cao Fengshun Lu |
| author_sort | Fukang Yin |
| collection | DOAJ |
| description | This paper develops a modified variational iteration method coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs). The approximate solutions of PDEs are calculated in the form of a series whose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wavelets coefficient matrices of the nonlinear terms. The main advantage of the new method is that it can avoid solving the nonlinear algebraic system and symbolic computation. Furthermore, the developed vector-matrix form makes it computationally efficient. The results show that the proposed method is very effective and easy to implement. |
| format | Article |
| id | doaj-art-576fff6ecd124f4187b0e4f2ff49b838 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-576fff6ecd124f4187b0e4f2ff49b8382025-02-03T01:21:39ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/157956157956Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential EquationsFukang Yin0Junqiang Song1Xiaoqun Cao2Fengshun 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, ChinaThis paper develops a modified variational iteration method coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs). The approximate solutions of PDEs are calculated in the form of a series whose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wavelets coefficient matrices of the nonlinear terms. The main advantage of the new method is that it can avoid solving the nonlinear algebraic system and symbolic computation. Furthermore, the developed vector-matrix form makes it computationally efficient. The results show that the proposed method is very effective and easy to implement.http://dx.doi.org/10.1155/2013/157956 |
| spellingShingle | Fukang Yin Junqiang Song Xiaoqun Cao Fengshun Lu Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations Journal of Applied Mathematics |
| title | Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations |
| title_full | Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations |
| title_fullStr | Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations |
| title_full_unstemmed | Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations |
| title_short | Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations |
| title_sort | couple of the variational iteration method and legendre wavelets for nonlinear partial differential equations |
| url | http://dx.doi.org/10.1155/2013/157956 |
| work_keys_str_mv | AT fukangyin coupleofthevariationaliterationmethodandlegendrewaveletsfornonlinearpartialdifferentialequations AT junqiangsong coupleofthevariationaliterationmethodandlegendrewaveletsfornonlinearpartialdifferentialequations AT xiaoquncao coupleofthevariationaliterationmethodandlegendrewaveletsfornonlinearpartialdifferentialequations AT fengshunlu coupleofthevariationaliterationmethodandlegendrewaveletsfornonlinearpartialdifferentialequations |