Computing the Decay of a Simple Reversible Sub-Markov Semigroup

Two different numerical methods for solving a non-self-adjoint evolution equation are compared in this paper. If the intial function lies in the domain of the operator, a recently proposed method that combines pseudospectral ideas and semigroup theory is shown to be considerably more accurate than a standard discretization method. One example is worked out in detail, but the methodsa used are of much wider applicability.