ABSTRACT
Since the time of Newton, physical phenomena have been investigated by writing them in the form of differential equations. Because the rate of change of a quantity is more easily determined than the quantity itself from a physical experiment, most physical laws of science and engineering are expressed in terms of differential equations. A differential equation is an equation that involves at least one derivative of some unknown function. In this chapter we shall be concerned with numerical methods for solving problems
of the form dy
dt = f(t, y) for a ≤ t ≤ b (12.1)
subject to an initial condition y(a) = y0.
