Collocation orthonormal Bernstein polynomials method for solving integral equations

Abstract EN

In this paper, we use a combination of Orthonormal Bernstein functions on the interval [0,1] for degree m = 5, and 6 to produce a new approach implementing Bernstein operational matrix of derivative as a method for the numerical solution of linear Fredholm integral equations and Volterra integral equations of the second kind.

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 the method to the exact solution.