Extrapolation for Solving a System of Weakly Singular Nonlinear Volterra Integral Equations of the Second Kind
Loizou, George and Lai, Choi-Hong and Khaliq, A. Q. M. and Sheng, Q.
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+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.
H. Han et al., "Extrapolation for Solving a System of Weakly Singular Nonlinear Volterra Integral Equations of the Second Kind," International Journal of Computer Mathematics, Taylor & Francis, Jan 2011.
The definitive version is available at http://dx.doi.org/10.1080/00207160.2011.606903
Mathematics and Statistics
Keywords and Phrases
system of weakly singular nonlinear Volterra integral equations of the second kind; extrapolation; a posteriori error estimate
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