{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:38:34Z","timestamp":1753886314613,"version":"3.41.2"},"reference-count":8,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,2,28]],"date-time":"2012-02-28T00:00:00Z","timestamp":1330387200000},"content-version":"vor","delay-in-days":58,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>The theory of approximate solution lacks  development in the area of nonlinear <jats:italic>q<\/jats:italic>\u2010difference 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 <jats:italic>q<\/jats:italic>\u2010polynomials are not easily found. In this paper, the formula for the multiplication of two <jats:italic>q<\/jats:italic>\u2010polynomials is presented. By applying the obtained results, we extend the use of the variational iteration method to nonlinear <jats:italic>q<\/jats:italic>\u2010difference equations. The numerical results reveal that the proposed method is very effective and can be applied to other nonlinear <jats:italic>q<\/jats:italic>\u2010difference equations.<\/jats:p>","DOI":"10.1155\/2012\/704138","type":"journal-article","created":{"date-parts":[[2012,2,28]],"date-time":"2012-02-28T21:04:40Z","timestamp":1330463080000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Application of the Variational Iteration Method to Strongly Nonlinear <i>q<\/i>\u2010Difference Equations"],"prefix":"10.1155","volume":"2012","author":[{"given":"Hsuan-Ku","family":"Liu","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,2,28]]},"reference":[{"key":"e_1_2_8_1_2","unstructured":"MuttelC. The Black Scholes eqaution in quantum calculus M.S. thesis 2007 University of Missouri-Rolla."},{"key":"e_1_2_8_2_2","first-page":"149","article-title":"Polynomial and series solutions of dynamic equations on time scales","volume":"12","author":"Haile B. D.","year":"2003","journal-title":"Dynamic Systems and Applications"},{"key":"e_1_2_8_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2009.01.033"},{"key":"e_1_2_8_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2006.07.009"},{"key":"e_1_2_8_5_2","unstructured":"KoornwinderT. H. q-Special functions: a tutorial arXiv:math\/9403216v1 1994."},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0201-1"},{"key":"e_1_2_8_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF03322019"},{"key":"e_1_2_8_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.02.048"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/704138.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/704138.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/704138","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T06:54:49Z","timestamp":1718088889000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/704138"}},"subtitle":[],"editor":[{"given":"Debasish","family":"Roy","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/704138"],"URL":"https:\/\/doi.org\/10.1155\/2012\/704138","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2011-07-30","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-11-30","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-02-28","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"704138"}}