Author(s)

Lian Chen, Junsheng Duan^*

School of Sciences, Shanghai Institute of Technology, Shanghai, China.

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 equations. 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 integration including fractional integral equations. Numerical tests verify the validity of the proposed schemes.

Volterra Integral Equation, Picard Iteration Method, Numerical Integration, Multistage Scheme

Chen, L. and Duan, J. (2015) Multistage Numerical Picard Iteration Methods for Nonlinear Volterra Integral Equations of the Second Kind. Advances in Pure Mathematics, 5, 672-682. doi: 10.4236/apm.2015.511061.