Collocation Orthonormal Berntein Polynomials method for Solving Integral Equations

Abstract

In this paper, we use a combination of Orthonormal Bernstein functions on the interval  for degree ,and 6 to produce anew approach implementing Bernstein Operational matrix of derivative as a method for the numerical solution of linear Fredholm integral equations of the second kind and Volterra integral equations. The method converges rapidly to the exact solution and gives very accurate results even by low value of m. Illustrative examples are included to demonstrate the validity and efficiency of the technique and convergence of method to the exact solution.

Keywords: Bernstein polynomials, Operational Matrix of Derivative, Linear Fredholm Integral Equations of the Second  Kind and Volterra Integral Equations.