Extrapolation for solving a system of weakly singular nonlinear Volterra integral equations of the second kind

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.

Keywords:

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

2010 AMS Subject Classifications :

• 45D05
• 45G05
• 45G15
• 65B05

Acknowledgements

This work is partially supported by the National Science Foundation of China (10671136, 10726018).