Discretization with variable time steps of an evolution equation with a positive-type memory term

We consider the linearized form of an evolution equation used to model viscoelasticity and heat conduction in materials with memory. The equation is discretized in time using several schemes based on the backward Euler and Crank-Nicolson methods, and incorporating appropriate quadratures for the memory term. By permitting variable time steps, we remove a restriction present in earlier related work by the first two authors.