Methods for Parallel Integration of Stii Systems of Odes

This paper presents a class of parallel numerical integration methods for stii systems of ordinary diierential equations which can be partitioned into loosely coupled subsystems. The formulas are called decoupled backward diierentiation formulas, and they are derived from the classical formulas by restricting the implicit part to the diagonal subsystem. 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. The main emphasis is on the formula of order 1, the decoupled implicit Euler formula. It is proved that this formula even for a wide range of multirate formulations has an asymptotic global error expansion permitting extrapolation. Besides, suucient conditions for absolute stability are presented.