Article citationsMore>>

Costarelli, D. and Spigler, R. (2013) Solving Volterra Integral Equations of the 2nd Kind by Sigmoidal Functions Approximations. Journal of Integral Equations and Applications, 25, 193-222.
http://dx.doi.org/10.1216/JIE-2013-25-2-193

has been cited by the following article:

• 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.