﻿ The solving linear one-dimemsional Volterra integral equations of the second kind in reproducing kernel space

# The solving linear one-dimemsional Volterra integral equations of the second kind in reproducing kernel space

##### نویسندگان
• A. Fazli Department of Mathematic, Science and Research Branch, Islamic Azad University, Tehran, Iran
• Sh. Javadi Department of Mathematic, Kharazmi University, Tehran, Iran.
##### چکیده

In this paper, to solve a linear one-dimensional Volterra  integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of  integral equation in terms of the basis functions. The examples presented in this paper show validity of the method. But this method does not provide results for nonlinear one-dimensional Volterra integral equations of the second kind. In this case for calculation Fourier cofficients the new method should be given. Thus the next focus on providing a method for calculating  Fourier  cofficients in the nonlinear mode. Also we think that this method can be generalized to linear two-dimensional Volterra integral equations of the second kind and we worked on this in the another paper.

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عنوان ژورنال:

دوره 3  شماره 12

صفحات  79- 86

تاریخ انتشار 2018-01-01

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