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...

Full description

Saved in:
Bibliographic Details
Main Author: Hsuan-Ku Liu
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/704138
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850230113315061760
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