Extrapolation for Solving a System of Weakly Singular Nonlinear Volterra Integral Equations of the Second Kind

Editor(s)

Loizou, George and Lai, Choi-Hong and Khaliq, A. Q. M. and Sheng, Q.

Abstract

This article discusses an extrapolation method for solving a system of weakly singular nonlinear Volterra integral equations of the second kind. Based on a generalization of the discrete Gronwall inequality and Navot's quadrature rule, the modified trapeziform quadrature algorithm is presented. The iterative algorithm for solving the discrete system possesses a high accuracy order O(h 2+α). After the asymptotic expansion of errors is proved, we can obtain an approximation with a higher accuracy order using extrapolation. An a posteriori error estimation is provided. Some numerical results are presented to illustrate the efficiency of our methods.

Department(s)

Mathematics and Statistics

Keywords and Phrases

system of weakly singular nonlinear Volterra integral equations of the second kind; extrapolation; a posteriori error estimate

International Standard Serial Number (ISSN)

0020-7160

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2011 Taylor & Francis, All rights reserved.

Publication Date

01 Jan 2011

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