Computing Exact Solutions of Initial Value Problems

Finding the exact solution of initial value problems is the main topic of this thesis. Because differential equations in practice can be hard to solve, we require algorithms to solve them on a computer. Since the solution of the equation needs to be stored on a computer, we first discuss the representation of real functions. We show that approximating a function by polynomials gives a suitable representation, and we prove that this representation is admissible. Finally, we discuss an algorithm described by Edalat, Lieutier and Krznarić which finds the exact solution of initial value problems, and we solve a simple equation with it. This algorithm works only for a certain class of differential equations, and hence extensions are required for more difficult problems.