A new approach for numerical solution of a linear system with distributed delays, Volterra delay-integro-differential equations, and nonlinear Volterra-Fredholm integral equation by Bezier curves

In this paper, we present Bezier curves method to solve Volterra delay-integro-differential equations. Also, this paper is concerned with a linear system with distributed input delay and input saturation. The approximation process by Bezier curves method is done in two steps. First we divide the time interval into 2k subintervals, second approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree n, and determine Bezier curves on any subinterval by n + 1 control points. Also, we have used Bezier curves method to solve linear and nonlinear Volterra-Fredholm integral equations, numerically. The proposed method is simple and computationally advantageous. Some numerical examples demonstrate the validity and applicability of the technique.