Ordinary differential equations

Abstract

In this chapter some methods for the numerical solution of ordinary differential equations are described. First-order equations, of the general form

$$y^{(n)} = f\left( {x,y,y', \ldots ,y^{(n - 1)} } \right)$$

((5.2))

or higher-order equations, which can be written

$$y^{(n)} = f(x,y,y', \ldots ,y^{(n - 1)} )$$

((5.2))

have solutions which may be written

$$y = \phi (x)$$

((5.3))

The problem is to determine, from (5.1) or (5.2) and the necessary boundary conditions, the relationaship (5.3) between x and y.