Computational Solutions to a Non-Uniform Time-Delay Linear System.

Two computational methods are considered for a class of non-uniform, continuous, multiple time-delay linear systems, which have been developed in the modeling of lossless layered media. The first approach discretizes the time axis and inserts states of intermediate delays, to arrive at a set of standard finite-difference equations. For our particular system, matrix multiplications can be reduced to simple scalar multiplications. The second approach defines mapping rules for the transformation of states at an interfaces, and keep a state reference table for look-up and branching. The procedure is similar to ray-tracing. Several experimental results are presented to show the trade-off between storage requirement and CPU time-spent for the two methods.