Integration of Partitioned Stii Systems of Ordinary Diierential Equations ?

Partitioned systems of ordinary diierential equations are in qualitative terms characterized as monotonically max-norm stable if each subsystem is stable and if the couplings from one subsystem to the others are weak. Each subsystem of the partitioned system may be discretized independently by the backward Euler formula using solution values from the other subsystems corresponding to the previous time step. The monotone max-norm stability guarantees this discretization to be stable. This so-called decoupled implicit Euler method is ideally suited for parallel computers. With one or several subsystems allocated to each processor, information only has to be exchanged after completion of a step but not during the solution of the nonlinear algebraic equations. This paper considers strategies and techniques for partitioning a system into a monotonically max-norm stable system. It also presents error bounds to be used in controlling stepsize, relaxation between subsystems and the validity of the partitioning. Finally a realistic example is presented .