The implication of hybrid Chebyshev polynomials for solving a class of integral equations based on the Galerkin method

Paria Assari¹

1) Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran,

Publication : 2nd. International Congress on science & Engineering - paris(parisconf.com)
Abstract :
The purpose of this study is to obtain a scheme for the numerical solution of Hammerstein integral equations of the second kind. Hammerstein integral equations have been arisen from mathematical models in various branches of applied sciences and engineering. The method approximates the solution using the hybrid Chebyshev polynomials in the Galerkin method. The method reduces the solution of these types of integral equations to the solution of a nonlinear system of algebraic equations. The algorithm of the presented approach is attractive and easy to implement on computers. The results of numerical experiments confirm the accuracy and efficiency of the new scheme presented in the current paper.
Keywords : Hammerstein integral equation; Chebychev polynomial; Hybrid function; Block-pulse function; Conver gence analysis