Numerical Methods

Abstract

In previous chapters analytical solution techniques to both ordinary and partial differential equations were presented. More often than not, problems are encountered for which the describing differential equations are extremely difficult, if not impossible, to solve analytically. Fortunately, since the latter part of the 1950s, the digital computer has become an increasingly useful tool for solving differential equations, whether they be ordinary or partial, linear or nonlinear, homogeneous or nonhomogeneous, or first order or tenth order. It is, of course, not always simple to solve a differential equation, or a set of differential equations, using numerical methods. A numerical technique can be very intricate and difficult to understand, requiring substantial computer capability. Some techniques exist only in the literature or in advanced texts on the subject. We will, however, present several of the simplest methods for solving both ordinary and partial differential equations.