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

سال انتشار: 1402
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 143

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شناسه ملی سند علمی:

JR_CMDE-11-1_002

تاریخ نمایه سازی: 15 بهمن 1401

چکیده مقاله:

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.

نویسندگان

Youssri Youssri

Department of Mathematics, Faculty of Science, Cairo University, Giza ۱۲۶۱۳, Egypt.

Shahenda Sayed

Department of Mathematics, Faculty of Science, Helwan University, Cairo ۱۱۷۹۵, Egypt.

Amany Mohamed

Department of Mathematics, Faculty of Science, Helwan University, Cairo ۱۱۷۹۵, Egypt.

Emad Aboeldahab

Department of Mathematics, Faculty of Science, Helwan University, Cairo ۱۱۷۹۵, Egypt.

Waleed Abd-Elhameed

Department of Mathematics, Faculty of Science, Cairo University, Giza ۱۲۶۱۳, Egypt.

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