The asymptotic behavior for numerical solution of a Volterra equation (Q1873580)

The author studies the long-time asymptotic stability and convergence properties for the numerical solution of a Volterra equation of parabolic type. The methods discussed are based on the first-second order backward difference methods. A discretization of the spatial partial differential operators by the finite element method is considered in their discussion. The memory term is approximated by the convolution quadrature and the interpolant quadrature.