Title of article :
Numerical solution of nonlinear two-dimensional Volterra integral equation of the second kind in the reproducing kernel space
Author/Authors :
Fazli, A. Department of Mathematic - Science and Research Branch - Islamic Azad University, Tehran, Iran , Allahviranloo, T. Department of Mathematic - Science and Research Branch - Islamic Azad University, Tehran, Iran , Javadi, Sh. Department of Mathematic - Kharazmi University, Tehran, Iran
Abstract :
In this article, an effective method is given to solve nonlinear two-dimensional Volterra integral equations of the second kind. First, we find the solution of integral equation in terms of reproducing kernel functions in series, then by truncating the series an approximate solution obtained. In addition, the calculation of Fourier coefficients solution of the integral equation in terms of reproducing kernel functions is notable. Numerical examples are presented, and their results are compared with the analytical solution to demonstrate the validity and applicability of the method
Keywords :
Two dimentional Volterra integral equation of the second kind , Reproducing kernel , Fourier coefficients
Journal title :
Mathematical Sciences
