On the Time-Domain Analysis of Linear Time-Invariant Networks with Large Time-Constant Spreads by Digital Computer

Abstract

The recent theoretical results of Liniger and Willoughby have been applied to the transient analysis of linear time-invariant networks possessing large time-constant spreads. In our approach we accept a compromise situation where an acceptable loss of integration accuracy for the slowly varying components of the solution (with respect to an arbitrarily specified integration time steph) is incurred, but where the rapidly varying components of the solution (again with respect toh) are proportionally "killed off." This is accomplished by the selection, in some optimal way, of a free parameter characterizing a family of linear one-step numerical integration formulas.