Multistage Numerical Picard Iteration Methods for Nonlinear Volterra Integral Equations of the Second Kind

Abstract

Using the Picard iteration method and treating the involved integration by numerical quadrature formulas, we propose a numerical scheme for the second kind nonlinear Volterra integral equa-tions. For enlarging the convergence region of the Picard iteration method, multistage algorithm is devised. We also introduce an algorithm for problems with some singularities at the limits of in-tegration including fractional integral equations. Numerical tests verify the validity of the pro-posed schemes.