Advances in Pure Mathematics

Volume 5, Issue 11 (September 2015)

ISSN Print: 2160-0368   ISSN Online: 2160-0384

Google-based Impact Factor: 0.62  Citations  h5-index & Ranking

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

HTML  XML Download Download as PDF (Size: 569KB)  PP. 672-682  
DOI: 10.4236/apm.2015.511061    4,041 Downloads   5,053 Views  Citations
Author(s)

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.

Share and Cite:

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.

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.