Introduction and study of fourth order theta schemes for linear wave equations
A new class of high order, implicit, three time step schemes for semi-discretized wave equations is introduced and studied. These schemes are constructed using the modified equation approach, generalizing the @q-scheme. Their stability properties are investigated via an energy analysis, which enables us to design super-convergent schemes and also optimal stable schemes in terms of consistency errors. Specific numerical algorithms for the fully discrete problem are tested and discussed, showing the efficiency of our approach compared to second order @q-schemes.
Deterministic network calculus (DNC) is not suitable for deriving performance guarantees for wireless networks due to their inherently random behaviors. In this paper, we develop a method for Quality of Service (QoS) analysis of wireless channels subject to Rayleigh fading based on stochastic network calculus. We provide closed-form stochastic service curve for the Rayleigh fading channel. With this service curve, we derive stochastic delay and backlog bounds. Simulation results verify that the bounds are reasonably tight. Moreover, through numerical experiments, we show the method is not only capable of deriving stochastic performance bounds, but also can provide guidelines for designing transmission strategies in wireless networks.