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Article
Extrapolation for Solving a System of Weakly Singular Nonlinear Volterra Integral Equations of the Second Kind
International Journal of Computer Mathematics
  • Huilei Han
  • Xiaoming He, Missouri University of Science and Technology
  • Yaping Liu
  • Tao Lü
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
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2011 Taylor & Francis, All rights reserved.
Publication Date
1-1-2011
Citation Information
Huilei Han, Xiaoming He, Yaping Liu and Tao Lü. "Extrapolation for Solving a System of Weakly Singular Nonlinear Volterra Integral Equations of the Second Kind" International Journal of Computer Mathematics (2011)
Available at: http://works.bepress.com/xiaoming-he/27/