Splines of the Fourth Order Approximation and the Volterra Integral Equations

This paper is a continuation of a series of papers devoted to the numerical solution of integral equations using local interpolation splines. The main focus is given to the use of splines of the fourth order of approximation. The features of the application of the polynomial and non-polynomial splines of the fourth order of approximation to the solution of Volterra integral equation of the second kind are discussed. In addition to local splines of the Lagrangian type, integro-differential splines are also used to construct computational schemes. The comparison of the solutions obtained by different methods is carried out. The results of the numerical experiments are presented.

Continuous Local Splines of the Fourth Order of Approximation and Boundary Value Problem

This paper discusses the construction of polynomialand non-polynomial splines of the fourth order of approximation.The behavior of the Lebesgue constants for the left, the right, andthe middle continuous cubic polynomial splines are considered.The non-polynomial splines are used for the construction of thespecial central difference approximation. The approximation offunctions, and the solving of the boundary problem with thepolynomial and non-polynomial splines are discussed. Numericalexamples are done.