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

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 step ) is incurred, but where the rapidly varying components of the solution (again with respect to ) 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.