The spatial discretization of initial-value problems for (nonlinear) parabolic or hyperbolic PDEs with memory terms leads to (large) systems of Volterra integro-differential equations (VIDEs). In this paper we study the efficient numerical solution of such systems by methods based on linear multistep formulas, using special factorization (or splitting) techniques in the iterative solution of the resulting (expensive) nonlinear algebraic equations. The analysis of the convergence and stability properties is complemented by numerical examples.

Modelling, Analysis and Simulation [MAS]
Computational Dynamics

Brunner, H., van der Houwen, P., & Sommeijer, B. (1999). Splitting methods for partial Volterra integro-differential equations. Modelling, Analysis and Simulation [MAS]. CWI.