Upper and lower bounds of conjugate points of fourth order linear differential equations

The main purpose of this paper is to present methods for approximating conjugate points of linear fourth order differential equations as well as various examples of results from these methods. We consider five examples of fourth order conjugate point problems. We use them to illustrate how each method works as well as how it performs. We compare the results obtained to the actual values of the conjugate points in question. Also included are the methods available for second order equations as well as examples of their use since these methods will motivate the methods for the fourth order case. In the last chapter a numerical method for computing conjugate points is discussed and illustrated.