Numerical Solution of Parabolic Volterra Integro-Differential Equations via Backward-Euler Scheme

摘要

In this study, we investigate convergence properties of time and space discretization of Parabolic Volterra integro-differential equations (PVIDE) is outlined. The rectangle and the trapezoidal rules applied for integral term of these equations and finite difference method (Backward-Euler method) used for partial differential part. The integral is approximated in each case by the quadrature rule with relatively high-order truncation error. We consider time step methods based on the backward-Euler method and combined with the appropriate quadrature rules.