Conventional Numerical Methods for Solving the Initial Value Problem

Abstract

Let us consider the following system of ordinary first-order differential equations

$$y'\, = \,f(x,y),$$

(1.1.1)

where y,f(x,y)ɛR^m, xɛ[a,b]. The function z=z(x) is called a solution of (1.1.1) if z is defined and differentiable for xɛ[a,b] and

$$z'\,(x)\, = \,f[x,z(x)].$$