TITLE:
Multistage Numerical Picard Iteration Methods for Nonlinear Volterra Integral Equations of the Second Kind
AUTHORS:
Lian Chen, Junsheng Duan
KEYWORDS:
Volterra Integral Equation, Picard Iteration Method, Numerical Integration, Multistage Scheme
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.5 No.11,
September
7,
2015
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 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.