  This paper is concerned with the adaptation of alternating direction implicit
(ADI) time discretization schemes for the numerical solution of partial
integro-differential equations (PIDEs) with application to the Bates model in
finance. Three different adaptations are formulated and their (von Neumann)
stability is analyzed. Ample numerical experiments are provided for the Bates
PIDE, illustrating the actual stability and convergence behaviour of the three
adaptations.
