Abstract
The partial differential equation that characterizes variable time delay is analyzed. Analytical solution methods are applicable when endpoint conditions and variable delay time are known in advance; two such methods are given. When variable time delay is but one part of a larger system, however, the simulation of the larger system on a computer can be facilitated by the use of finite difference approximations of the variable delay element. A class of variable delay approximations is developed from which several commonly used approximations follow as special cases. A particular approximation having truncation error of the order of ( Δx) 4 is found to be near optimum. Simulation results are presented.
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