AN ANALOGUE TO THE A(θ)-STABILITY CONCEPT FOR IMPLICIT-EXPLICIT BDF METHODS

For implicit-explicit multistep schemes, using a suitable form of Dahlquist's test equation, we introduce an analogue to the A(theta)-stability concept, valid for implicit methods, and formulate a stability criterion in terms of an auxiliary function that plays a key role in our analysis. Furthermore, for implicit-explicit backward difference formula methods, we either evaluate the auxiliary function or establish very good estimates of it; as a result, we derive a sharp or very good unconditional stability condition, respectively, the analogue of the determination of the exact angle theta for implicit methods or of a good approximation thereof. A comparison with the corresponding necessary stability condition provides evidence of the quality of the sufficient stability condition. In addition, we verify our analysis with results of a series of numerical experiments.