ON A WAY FOR SOLVING VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND

Abstract

There are many classes’ methods for finding of the approximately solution of Volterra integral equations of the second kind. Recently, the numerical methods have been developed for solving the integral equations of Volterra type, which is associated with the using of computers. Volterra himself suggested quadrature formula for finding the numerical solution of integral equation with the variable bounders. By using some disadvantages of mentioned methods here proposed to use some modifications of the quadrature formula which have called as the multistep methods with the fractional step-size. This method has comprised with the known methods and found some relation between constructed here methods with the hybrid methods. And also, the advantages of these methods are shown. Constructed some simple methods with the fractional step-size, which have the degree p≤4 of the receiving results. Here is applied one of suggested methods to solve some model problem and receive results, which are corresponding to theoretical results