Integration of Partitioned Stiff Systems of Ordinary Differential Equations ⋆

Abstract. Partitioned systems of ordinary differential equations are in qualitative terms characterized as monotonically max-norm stable if each sub-system is stable and if the couplings from one sub-system to the others are weak. Each sub-system of the partitioned system may be discretized independently by the backward Euler formula using solution values from the other sub-systems 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 sub-systems 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 sub-systems and the validity of the partitioning. Finally a realistic example is presented.