A new high-order absolutely-stable explicit numerical integration algorithm for the time-domain simulation of nonlinear circuits

Abstract

A new numerical integration method for the time domain simulation of nonlinear circuits is presented. The new method does not belong to the traditional class of linear multistep methods. Consequently it is free from Dahlquist's barriers in terms of stability and order. The new method is shown to be both A-stable and at the same time of arbitrarily high order. In addition, the method is explicit in nature and does not require matrix inversion at each time step. Examples of linear and nonlinear circuit simulation are included. The proposed method significantly speeds up the time domain simulation of nonlinear circuits as it combines the efficiency of an explicit method with the accuracy and large step size possible with high order.