Extrapolation for Solving a System of Weakly Singular Nonlinear Volterra Integral Equations of the Second KindInternational Journal of Computer Mathematics
Editor(s)Loizou, George and Lai, Choi-Hong and Khaliq, A. Q. M. and Sheng, Q.
AbstractThis 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+Î±). 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,
- a posteriori error estimate
Document TypeArticle - Journal
Rights© 2011 Taylor & Francis, All rights reserved.
Citation InformationHuilei 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/