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Youssri, Youssri, Sayed, Shahenda, Mohamed, Amany, Aboeldahab, Emad, Abd-Elhameed, Waleed. (1401). Modified Lucas polynomials for the numerical treatment of second-order boundary value problems. سامانه مدیریت نشریات علمی, (), -. doi: 10.22034/cmde.2022.50891.2115
Youssri H. Youssri; Shahenda Sayed; Amany Saad Mohamed; Emad Aboeldahab; Waleed Mohamed Abd-Elhameed. "Modified Lucas polynomials for the numerical treatment of second-order boundary value problems". سامانه مدیریت نشریات علمی, , , 1401, -. doi: 10.22034/cmde.2022.50891.2115
Youssri, Youssri, Sayed, Shahenda, Mohamed, Amany, Aboeldahab, Emad, Abd-Elhameed, Waleed. (1401). 'Modified Lucas polynomials for the numerical treatment of second-order boundary value problems', سامانه مدیریت نشریات علمی, (), pp. -. doi: 10.22034/cmde.2022.50891.2115
Youssri, Youssri, Sayed, Shahenda, Mohamed, Amany, Aboeldahab, Emad, Abd-Elhameed, Waleed. Modified Lucas polynomials for the numerical treatment of second-order boundary value problems. سامانه مدیریت نشریات علمی, 1401; (): -. doi: 10.22034/cmde.2022.50891.2115

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  XML اصل مقاله (1.35 MB)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.50891.2115
نویسندگان
Youssri H. Youssri email orcid 1؛ Shahenda Sayed2؛ Amany Saad Mohamed2؛ Emad Aboeldahab2؛ Waleed Mohamed Abd-Elhameedorcid 3
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
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تعداد مشاهده مقاله: 1,050
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