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

Abstract

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.