Application of the Variational Iteration Method to Strongly Nonlinear 𝑞-Difference Equations
The theory of approximate solution lacks development in the area of nonlinear 𝑞-difference equations. One of the difficulties in developing a theory of series solutions for the homogeneous equations on time scales is that formulas for multiplication of two 𝑞-polynomials are not easily found. In thi...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/704138 |
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| author | Hsuan-Ku Liu |
| author_facet | Hsuan-Ku Liu |
| author_sort | Hsuan-Ku Liu |
| collection | DOAJ |
| description | The theory of approximate solution lacks development in the area of nonlinear 𝑞-difference equations. One of the difficulties in developing a theory of series solutions for the homogeneous equations on time scales is that formulas for multiplication of two 𝑞-polynomials are not easily found. In this paper, the formula for the multiplication of two 𝑞-polynomials is presented. By applying the obtained results, we extend the use of the variational iteration method to nonlinear 𝑞-difference equations. The numerical results reveal that the proposed method is very effective and can be applied to other nonlinear 𝑞-difference equations. |
| format | Article |
| id | doaj-art-20fd007f31234c71b5b9274ca77db9d1 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-20fd007f31234c71b5b9274ca77db9d12025-08-20T02:03:58ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/704138704138Application of the Variational Iteration Method to Strongly Nonlinear 𝑞-Difference EquationsHsuan-Ku Liu0Department of Mathematics and Information Education, National Taipei University of Education, Taipei 106, TaiwanThe theory of approximate solution lacks development in the area of nonlinear 𝑞-difference equations. One of the difficulties in developing a theory of series solutions for the homogeneous equations on time scales is that formulas for multiplication of two 𝑞-polynomials are not easily found. In this paper, the formula for the multiplication of two 𝑞-polynomials is presented. By applying the obtained results, we extend the use of the variational iteration method to nonlinear 𝑞-difference equations. The numerical results reveal that the proposed method is very effective and can be applied to other nonlinear 𝑞-difference equations.http://dx.doi.org/10.1155/2012/704138 |
| spellingShingle | Hsuan-Ku Liu Application of the Variational Iteration Method to Strongly Nonlinear 𝑞-Difference Equations Journal of Applied Mathematics |
| title | Application of the Variational Iteration Method to Strongly Nonlinear 𝑞-Difference Equations |
| title_full | Application of the Variational Iteration Method to Strongly Nonlinear 𝑞-Difference Equations |
| title_fullStr | Application of the Variational Iteration Method to Strongly Nonlinear 𝑞-Difference Equations |
| title_full_unstemmed | Application of the Variational Iteration Method to Strongly Nonlinear 𝑞-Difference Equations |
| title_short | Application of the Variational Iteration Method to Strongly Nonlinear 𝑞-Difference Equations |
| title_sort | application of the variational iteration method to strongly nonlinear 𝑞 difference equations |
| url | http://dx.doi.org/10.1155/2012/704138 |
| work_keys_str_mv | AT hsuankuliu applicationofthevariationaliterationmethodtostronglynonlinearqdifferenceequations |