Collocation Orthonormal Bernstein Polynomials Method for Solving Integral Equations
Abstract
In this paper, we use a combination of Orthonormal Bernstein functions on the interval [0,1] for degree m=5,and 6 to produce anew 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.
Keywords
Bernstein polynomials, Operational Matrix ofDerivative, Linear Fredholm Integral Equations of the Second Kind and Volterra Integral EquationsMetrics