Bernstein Operational Matrix Approach for Integro-Differential Equation Arising in Control theory

Abstract

The aim of this paper is to propose an efficient numerical method for solving the integro-differential equations arising in many braches of sciences using Bernstein polynomials. This algorithm based on Bernstein polynomials approximation for integro-differential equations. First, Bernstein operational matrix of differentiation is derived using Bernstein polynomials and then applied to solve integro-differential equations. The solutions obtained by proposed method indicate that the approach is easy to implement and computationally very attractive. A good agreement between the obtained solution and some well-known results has been obtained. Two numerical examples are provided to show the advantage of using Bernstein operational matrix. This method is capable of greatly reducing the size of calculations while still maintaining high accuracy of the numerical solution.