{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T07:04:39Z","timestamp":1763017479988},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>- In this paper, a novel modification of the spectral-homotopy analysis method (SHAM) technique for solving highly nonlinear initial value problems that model systems with chaotic and hyper-chaotic behaviour is presented. The proposed method is based on implementing the SHAM on a sequence of multiple intervals thereby increasing it\u2019s radius of convergence to yield highly accuratemethod which is referred to as the piece-wise spectral homotopy analysis method (PSHAM). We investigate the application of the PSHAM to the L\u00a8u system [20] which is well known to display periodic, chaotic and hyper-chaotic behaviour under carefully selected values of it\u2019s governing parameters. Existence and uniqueness of solution of SHAM that give a guarantee of convergence of SHAM, has been discussed in details. Comparisons are made between PSHAMgenerated results and results from literature and Runge-Kutta generated results and good agreement is observed.<\/jats:p>","DOI":"10.1515\/jnma-2014-0015","type":"journal-article","created":{"date-parts":[[2014,11,25]],"date-time":"2014-11-25T08:29:57Z","timestamp":1416904197000},"source":"Crossref","is-referenced-by-count":3,"title":["On the piecewise-spectral homotopy analysis method and its convergence: solution of hyperchaotic L\u00fc system"],"prefix":"10.1515","volume":"22","author":[{"given":"S. S.","family":"Motsa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H. Saberi","family":"Nik","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"Effati","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Saberi-Nadjafi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","container-title":["Journal of Numerical Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/jnma-2014-0015\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T01:36:18Z","timestamp":1619055378000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/jnma-2014-0015\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,1]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.1515\/jnma-2014-0015","relation":{},"ISSN":["1569-3953","1570-2820"],"issn-type":[{"value":"1569-3953","type":"electronic"},{"value":"1570-2820","type":"print"}],"subject":[],"published":{"date-parts":[[2014,1,1]]}}}