Legendre polynomial solutions of higher order linear differential and integro-differential equations

This thesis consists of four chapters. The first chapter is devoted to the introduction. The second deals with the preliminaries, necessary fundamental definitions that will be need for later use. Original results are contained in the third and fourth section. In the third section, a new method called ?Legendre Collocation? for the Legendre polynomial solutions of higher order linear differential and integro-differential equations was presented. In the fourth section, examples of these kinds of equations were solved by using this new method, error analysis was done and graphics were drawn. In addition, we conclude that this new method works well and it can be suitable by examining error analysis of examples.