The present article is one of a number of articles in which the authors study the properties of integro-differential splines. The paper deals with the construction of integro-differential polynomial and nonpolynomial splines of the fifth order. The order of approximation with integrodifferential polynomial and nonpolynomial splines of the fifth order are given. We use the tensor product of polynomial and non-polynomial splines constructed in this paper for the approximation of functions of two variables. The results of these numerical experiments are given.

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.

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