New Numerical Approach for Solving Abel’s Integral Equations

• Autorzy: Anapalı Şenel Ayşe , Öztürk Yalçın , Gülsu Mustafa

Identyfikatory

DOI

10.2478/fcds-2021-0017

• Języki publikacji: EN

Abstrakty

EN

In this article, we present an efficient method for solving Abel’s integral equations. This important equation is consisting of an integral equation that is modeling many problems in literature. Our proposed method is based on first taking the truncated Taylor expansions of the solution function and fractional derivatives, then substituting their matrix forms into the equation. The main character behind this technique’s approach is that it reduces such problems to solving a system of algebraic equations, thus greatly simplifying the problem. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method. Figures and tables are demonstrated to solutions impress. Also, all numerical examples are solved with the aid of Maple.

Słowa kluczowe

EN

integral equations; singular integral equations; approximate solutions; collocation method; Taylor series

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Computing and Decision Sciences
• Rocznik: 2021
• Tom: Vol. 46, No. 3
• Strony: 255--271
• Opis fizyczny: Bibliogr. 28 poz., rys., tab.

Twórcy

autor

Anapalı Şenel Ayşe

• Department of Mathematics, Faculty of Science, Muğla Sıtkı Koçman University Mugla, Turkey

autor

Öztürk Yalçın

• Ula Ali KOÇMAN Vocational Scholl Muğla Sıtkı Koçman University, Mugla, Turkey

autor

Gülsu Mustafa

• Department of Mathematics, Faculty of Science, Muğla Sıtkı Koçman University Mugla, Turkey

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).