Palusinski This research applies spectral techniques to the time domain simulation of integrated circuits. The methods have been used to compute transient effects in multiple transmission lines. They are based on the expansion of unknown variables in the Chebyshev series. This assures very compact representation of waveforms, thus reducing computational penalties imposed by data interchange in relaxation methods. Tasks include: 1. Modeling of MOS circuits based on modified nodal analysis; 2. Application of spectral algorithms to bipolar circuits with various model switching strategies; 3. Construction of an efficient spectral algorithm for computation of transients in lossy transmission lines with frequency dependent parameters and nonlinear termination networks; 4. Using spectral techniques in a relaxation framework.