Про деякі результати дослідження інтегрального методу розв’язування лінійних диференціальних рівнянь

Abstract

The article considers the application of the integrated method for solving linear differential equations. An important prerequisite for using this approach is the possibility of reducing different types of ordinary differential equations to equivalent Volterra integral equations, while the inverse transformation is not always possible. The advantages of integral equations in the computational plan are determined by the smoothing properties of the integral operators, which is manifested in the increased accuracy of the obtained solutions or in the reduced number of computational operations in the process of their solution. In addition, integral equations allow solving problems were given or required functions have breaks of the first kind. From a more general point of view, when solving differential equations, increasing the error of the right part entails a rapid increase in the errors of the results together with increasing the rate of their accumulation, and the smoothing properties of the integrated method, due to the stability of direct methods. conditions of errors in the right part of the differential equation. The positive properties and efficiency of the integrated approach for solving linear differential equations are considered based on computational experiments, which allow to practically prove the expediency of using integrated methods of description and analysis of applied problems