Numerical method for the solution of linear boundary-value problem for integrodifferential equations based on spline approximations

Abstract

UDC 517.642
We propose a numerical method for the solution of linear boundary-value problem for system of integrodifferential equations. This method is based on the approximation of the integral term by a cubic spline and reduction of the original problem to a linear boundary-value problem for a system of loaded differential equations. We also propose new algorithms for finding the numerical solution and a method for the construction of approximate solution to the approximating boundary-value problem.