Graphical Solutions for the Characteristic Roots of the First Order Linear Differential-Difference Equation

[+] Author and Article Information
G. M. Sandquist

Mechanical Engineering, University of Utah, Salt Lake City, Utah 84112

V. C. Rogers

Ford, Bacon & Davis Utah, Inc., Salt Lake City, Utah 84102

J. Dyn. Sys., Meas., Control 101(1), 37-43 (Mar 01, 1979) (7 pages) doi:10.1115/1.3426394 History: Received August 16, 1978; Revised January 23, 1979; Online July 13, 2010


Approximate values for all the apparent real and imaginary characteristic roots of the general first order linear differential-difference equation are determined (primarily graphically) without mathematical proof. These approximate values may then be iterated in a convergent form of the characteristic equation to provide any desired numerical accuracy as shown in several examples. A practical application involving the kinetic behavior of nuclear reactor systems with delayed neutrons is given and compared with the more familiar system solutions.

Copyright © 1979 by ASME
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