<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

New Numerical Approach for Solving Abel’s Integral Equations

Department of Mathematics, Faculty of Science

Ula Ali KOÇMAN Vocational Scholl Muğla Sıtkı Koçman University

Foundations of Computing and Decision Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"New Numerical Approach for Solving Abel\u2019s Integral Equations"}

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...

New Numerical Approach for Solving Abel’s Integral Equations

Data publikacji: 17 wrz 2021

Zakres stron: 255 - 271

Otrzymano: 14 cze 2020

Przyjęty: 22 mar 2021

DOI: https://doi.org/10.2478/fcds-2021-0017

Słowa kluczowe
Integral equations, singular integral equations, generalized Taylor series, approximate solutions, collocation method

© 2021 Ayşe Anapalı Şenel et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

New Numerical Approach for Solving Abel’s Integral Equations

Data publikacji: 17 wrz 2021

Zakres stron: 255 - 271

Otrzymano: 14 cze 2020

Przyjęty: 22 mar 2021

DOI: https://doi.org/10.2478/fcds-2021-0017

Słowa kluczoweIntegral equations, singular integral equations, generalized Taylor series, approximate solutions, collocation method

© 2021 Ayşe Anapalı Şenel et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Słowa kluczowe
Integral equations, singular integral equations, generalized Taylor series, approximate solutions, collocation method