Numerical solution of differential equations of Lane-Emden type by Gegenbauer and rational Gegenbauer collocation methods | ||
| Computational Mathematics and Computer Modeling with Applications (CMCMA) | ||
| دوره 1، شماره 1، شهریور 2022، صفحه 69-85 اصل مقاله (340.91 K) | ||
| نوع مقاله: Regular paper | ||
| شناسه دیجیتال (DOI): 10.52547/CMCMA.1.1.69 | ||
| نویسندگان | ||
| Fatemeh Baharifard* 1؛ Kourosh Parand2 | ||
| 1School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran | ||
| 2Department of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran | ||
| چکیده | ||
| In this paper, we apply the collocation method for solving some classes of Lane-Emden type equations that are determined in interval $[0, 1]$ and semi-infinite domain. We use an orthogonal system of functions, namely Gegenbauer polynomials and introduce the shifted Gegenbauer polynomials and the rational Gegenbauer functions as basis functions in the collocation method for problems in interval $[0, 1]$ and semi-infinite domain, respectively. We estimate that the proposed method has super-linear convergence rate and also investigate the Gegenbauer parameter $ (\alpha)$ to get more accurate answers for various Lane-Emden type problems. The comparison between the proposed method and other numerical results shows that the method is efficient and applicable. | ||
| کلیدواژهها | ||
| Gegenbauer polynomials؛ Rational Gegenbauer functions؛ Collocation method؛ Nonlinear ODE؛ Lane-Emden equations؛ Astrophysics | ||
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آمار تعداد مشاهده مقاله: 38 تعداد دریافت فایل اصل مقاله: 176 |
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