Second-order method for Parabolic Volterra Integral Equations with Crank-Nicolson Method

Ali Filiz

In this paper using Crank-Nicolson method we investigate convergence properties of time discretization of Parabolic Volterra integral equations are studied. The rectangle, the trapezoidal and Simpson’s rules applied for these equations. The integral is approximated in each case by the quadrature rule. The main idea of this paper quadrature rules based a fewer points, reducing the number of time levels at which the data need to be saved. We consider time step methods based on Crank-Nicolson method and combined with the appropriate quadrature rules.