On modified computing schemes of the spline-collocation method for solving integral equations of the second kind

Abstract

The Intelligent Support System (ISS) for approximate solving of the Fredholm and Volterra integral equations (IE) of the second kind (ISS IE) utilizes the following results: computing algorithms of spline-collocations method for solving the Fredholm and Volterra IE of the second kind, which essentially use the linear splines as basic functions for modeling and presenting the unknown solutions; a theoretical substantiation of the developed computing algorithms, obtained in the space of continuous functions and in the H¨older spaces, which is based on the results of function approximation with its linear polygons…