{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T15:53:00Z","timestamp":1759938780804,"version":"3.41.2"},"reference-count":22,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,5,26]],"date-time":"2011-05-26T00:00:00Z","timestamp":1306368000000},"content-version":"vor","delay-in-days":145,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>We extend a \n                  collocation method for solving a nonlinear \n                  ordinary differential \nequation (ODE) via Jacobi polynomials. To date, researchers \nusually use Chebyshev or Legendre collocation method for solving \nproblems in chemistry, physics, and so forth, see the works of (Doha and Bhrawy 2006, Guo 2000, and Guo et al. 2002). Choosing the optimal polynomial for solving every ODEs problem \ndepends on many factors, for example, smoothing continuously and \nother properties of the solutions. In this paper, we show \nintuitionally that in some problems choosing other members of \nJacobi polynomials gives better result compared to Chebyshev or \nLegendre polynomials.<\/jats:p>","DOI":"10.1155\/2011\/673085","type":"journal-article","created":{"date-parts":[[2011,5,26]],"date-time":"2011-05-26T19:33:14Z","timestamp":1306438394000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations"],"prefix":"10.1155","volume":"2011","author":[{"given":"Ahmad","family":"Imani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Azim","family":"Aminataei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ali","family":"Imani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,5,26]]},"reference":[{"volume-title":"Orthogonal Polynomials","year":"1985","author":"Szeg G.","key":"e_1_2_5_1_2"},{"volume-title":"The Special Functions and Their Approximations","year":"1969","author":"Luke Y.","key":"e_1_2_5_2_2"},{"key":"e_1_2_5_3_2","doi-asserted-by":"publisher","DOI":"10.1088\/0305\u20104470\/35\/15\/308"},{"key":"e_1_2_5_4_2","doi-asserted-by":"publisher","DOI":"10.1088\/0305\u20104470\/37\/3\/010"},{"key":"e_1_2_5_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(97)00228-8"},{"key":"e_1_2_5_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970425"},{"key":"e_1_2_5_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-84108-8"},{"volume-title":"Spectral Methods for Partial Differential Equations","year":"1984","author":"Voigt R. 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