New Algorithm for the System of Nonlinear Weakly Singular Volterra Integral Equations of the Second Kind and Integro-differential Equations

This paper presents a high accuracy quadrature method for solving the integro-differential equations and the system of weakly singular nonlinear Volterra integral equations of the second kind. These equations are important in many physical, biological and engineering models. Using Richardson extrapolation, an approximation with a higher accuracy order can be obtained. An a posteriori error estimation is provided. Some numerical results are presented to show the efficiency of our methods

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

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\u27s 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