Numerical Techniques

Abstract

As suggested in the previous chapter, in order for a numerical integration method to be reliable and efficient when used to solve the types of differential equation systems generated from circuit descriptions, the method must have several strong properties. For this reason, general purpose circuit simulation programs, like SPICE2[2] and ASTAP[3], use very robust numerical integration algorithms, members of the class of implicit multistep integration methods. In the first section of this chapter we will introduce this important class of methods, and demonstrate their use in a simple but nontrivial circuit example. The robustness of the implicit multistep integration algorithms will be demonstrated in Section 2, by proving that the implicit methods used for circuit simulation have the three key properties described in Chapter 2: charge conservation, exhaustive domain of dependence and stiff stability.