Bernstein polynomials iterative method for weakly singular and fractional Fredholm integral equations

Abstract. A novel iterative method based on Picard iterations and Berstein polynomials is proposed for solving weakly singular and fractional Fredholm integral equations. On a uniform mesh, at each iterative step a Bernstein type spline is constructed by using the values computed at the previous step. The error estimates are obtained in terms of the Lipschitz constants and the convergence of the method is proved. Some numerical examples are presented in order to illustrate the accuracy of this iterative method. Mathematics Subject Classification (2010): 65R20. Keywords: Weakly singular and fractional Fredholm integral equations, iterative numerical method, piecewise Bernstein polynomials spline, order of convergence.