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Modified Lucas polynomials for the numerical treatment of second-order boundary value problems | ||
Computational Methods for Differential Equations | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 17 تیر 1401 اصل مقاله (1.35 MB) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22034/cmde.2022.50891.2115 | ||
نویسندگان | ||
Youssri H. Youssri ![]() ![]() ![]() | ||
1Department of Mathematics, Faculty of Science, Cairo University, Giza-Egypt | ||
2Department of Mathematics, Faculty of Science, Helwan University, Cairo 11795, Egypt | ||
3Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt | ||
چکیده | ||
This paper is devoted to the construction of certain polynomials related to Lucas polynomials, namely, modified Lucas polynomials. The constructed modified Lucas polynomials are utilized as basis functions for the numerical treatment of the linear and non-linear second-order boundary value problems (BVPs) involving some specific important problems such as singular and Bratu-type equations. To derive our proposed algorithms, the operational matrix of derivatives of the modified Lucas polynomials is established by expressing the first-order derivative of these polynomials in terms of their original ones. The convergence analysis of the modified Lucas polynomials is deeply discussed by establishing some inequalities concerned with these modified polynomials. Some numerical experiments accompanied by comparisons with some other articles in the literature are presented to demonstrate the applicability and accuracy of the presented algorithms. | ||
کلیدواژهها | ||
Lucas polynomials؛ Boundary value problems؛ Spectral methods؛ Operational matrix؛ Convergence analysis | ||
آمار تعداد مشاهده مقاله: 1,050 تعداد دریافت فایل اصل مقاله: 174 |