The combined reproducing kernel method and Taylor series to solve nonlinear Abel's integral equations with weakly singular kernel

The reproducing kernel method and Taylor series to determine a solution for nonlinear Abel's integral equations are combined. In this technique, we first convert it to a nonlinear differential equation by using Taylor series. The approximate solution in the form of series in the reproducing ker...

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Bibliographic Details
Published in:Cogent mathematics 2016-12, Vol.3 (1), p.1250705
Main Authors: Alvandi, Azizallah, Paripour, Mahmoud
Format: Article
Language:English
Subjects:
Abel's integral
Estimating techniques
Integral equations
Kernels
Nonlinear differential equations
Nonlinear equations
reproducing kernel
Taylor series
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Summary:The reproducing kernel method and Taylor series to determine a solution for nonlinear Abel's integral equations are combined. In this technique, we first convert it to a nonlinear differential equation by using Taylor series. The approximate solution in the form of series in the reproducing kernel space is presented. The advantages of this method are as follows: First, it is possible to pick any point in the interval of integration and as well the approximate solution. Second, numerical results compared with the existing method show that fewer nodes are required to obtain numerical solutions. Furthermore, the present method is a reliable method to solve nonlinear Abel's integral equations with weakly singular kernel. Some numerical examples are given in two different spaces.
ISSN:2331-1835
2331-1835
2768-4830
DOI:10.1080/23311835.2016.1250705