Solving Linear Second Order Delay Differential Equations by Steps Method

Abstract

This thesis concentrates on steps method to solve delay differential equations (DDEs) with a single constant delay and constant coefficients. In this study the stability type of second order delay differential equation at equilibrium point is being considered where each coefficients are in R. First, the general stability theory for delay differential equations was highlighted before giving an in-depth stability analysis of the equation of harmonic oscillator. It turns out that a Theorem of Pontryagin (1908 -1988) is really helpful for answering these stability questions. Due to this Theorem all values for each coefficients in R, are determined such that equilibrium point is asymptotically stable for damped harmonic oscillator. However, this does not cover the stability type at equilibrium point for all coefficients. So more analysis was done in order to give a full answer of the stability problem. Finally comparing of analytical solution obtained by steps method with codes from Matlab solver DDE23 are shown.