Convergence analysis of non-polynomial spline functions for the Fredholm integral equation

Abstract

ABSTRACTIn our knowledge so far, the Non-polynomial Spline functions (NPS) have not been yet applied for approximating the integral equations. In this article, we want to use such functions for obtaining numerical solutions of Fredholm integral equations of the second kind. In our approach, the coefficients of the non polynomial spline are obtained by solving a system of linear equations. Finally, these functions are utilized to reduce the Fredholm integral equations to the solution of algebraic equations. Analysis of convergence is investigated. At the end, our test examples are presented to show the effectiveness of the method.