ABSTRACT
This chapter illustrates a fundamental thought process that must be used when doing any numerical modelling. It demonstrates how differential equations may be approximated; the applications in engineering and physics are three dimensional. The chapter describes the methods that may be brought to bear on nonlinear ordinary boundary-value problems. Ordinary differential equations are solved by the creative use of the finite-difference method, which reduces the differential equations to the evaluation of the roots of a system of simultaneous algebraic equations. It is shown that central differences should be used where convenient, while forward and backward differences should be used only near the boundaries of the region. Since the basic methodology has been developed in the preceding chapters, the chapter is concerned with the solution of ordinary differential equations and the solution strategies that are used.
