Chapter 1 Linear Difference Equations

This chapter constitutes an introduction to linear multi step methods, Runge Kutta methods, and finite difference methods which are presented in the chapters that follow. The homo- geneous and non-homogeneous linear difference equations are solved by the following Mathematica modulae: The module differenceEqn finds the general solution of a linear difference equation, the module baseSolution finds the fundamental set of solutions of a homogeneous linear difference equa- tion, the module particularSolution finds a particular solution of a non-homogeneous linear difference equation by the method of variation of coefficients. The chapter ends with a set of questions.