Numerical Methods

Abstract

The purpose of this chapter is to provide a brief introduction as to how a first- or second-order differential equation may be solved to the desired precision by using numerical methods like Euler’s method and fourth-order Runge–Kutta method. Emphasis is placed on the difference between an analytical and a numerical solution. Movement of a pendulum for an arbitrary amplitude is calculated numerically to exemplify how easily some problems can be solved by numerical methods. Methods for solving partial differential equations are also described, but are not used until a later chapter. The importance of testing, reproducibility and documentation of successive program versions are discussed. Specimen programs are given at the end of the chapter.