Modified Lucas polynomials for the numerical treatment of second-order boundary value problems

Youssri, Youssri Hassan; Sayed, Shahenda; Mohamed, Amany Saad; Aboeldahab, Emad; Abd-Elhameed, Waleed Mohamed

doi:10.22034/cmde.2022.50891.2115

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	Modified Lucas polynomials for the numerical treatment of second-order boundary value problems
Computational Methods for Differential Equations
مقاله 2، دوره 11، شماره 1، فروردین 2023، صفحه 12-31 اصل مقاله (570.53 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.50891.2115
نویسندگان
Youssri Hassan Youssri ¹؛ Shahenda Sayed²؛ Amany Saad Mohamed²؛ Emad Aboeldahab²؛ Waleed Mohamed Abd-Elhameed ¹
¹Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt.
²Department of Mathematics, Faculty of Science, Helwan University, Cairo 11795, 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؛ Bratu equations؛ Singular initial value problems؛ Spectral methods؛ Operational matrix؛ Convergence analysis

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Modified Lucas polynomials for the numerical treatment of second-order boundary value problems