CHAPTER 7 - Relaxation Methods

Abstract

This chapter elaborates the different aspects of relaxation methods. The problems considered includes the solution of a system of linear algebraic equations, the solution of second-order ordinary differential equations with two-point boundary conditions, and the solution of Laplace's or Poisson's elliptic partial differential equation. The same concepts and terms are used for these apparently different problems. In each case, two approaches are given which includes one suitable for hand or desk computations and one for digital computers. It is found that although the digital computer methods are obviously more important, the beginner would be well advised to try some hand computation methods in order to acquire some experience and insight into relaxation problems and because these techniques are often the starting point of the more important methods. On a digital computer this work would be carried out differently as it no longer saves time to restrict the arithmetic to small integers.