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.