Passivity considerations in stability studies of numerical integration algorithms

In this paper we introduce the concept of algorithmic passiv- in in ity and indicate its role in circuit and timing simulation programs. Algorithmic passivity shows the overall stability--or lack thereof--inherent in forward Euler, backward Euler, and trapezoidal one-step integration approximations as well as Gear's two-step method. Passivity can be applied to - Vi_ _ Vn-i+ i integration algorithms to provide sufficient conditions for the overall stability of simulation programs that may employ them on an intermixed basis.