Solution of the delayed single degree of freedom system equation by exponential matrix method

In this paper, an exponential collocation method for the solution linear delay differential equations with constant delay is presented. The utility of this matrix based method is that it is very systematic and by writing a Maple program, any type of second order linear differential delay equation can be solved easily. The method is applied to three different types of delay equations; linear oscillator with delay (i) in the restoring force term, (ii) in the damping term, and (iii) in the acceleration term. Time response curves have been plotted for each type and the effect of the parameters of the delay terms has been shown. An error analysis based on residual function is carried out to show the accuracy of the results.