ABSTRACT
In this chapter we are going to solve a common engineering problem: the initial value problem. Besides the formulation of a solution methodology, we will evaluate stability of the solution method.
The Euler method is a simple way of solving a differential equation. If the following ODE (ordinary differential equation) is given:
dx
dt = f(x, t) (7.1)
with the initial condition x(t = 0) = x0, we could generate an estimate of x at t+ δt as
x(t+ δt) = x(t) + dx
dt δt = x(t) + f(x, t)δt, (7.2)
so we can step forward in time, by evaluating the gradient, from the current step to the next step. Figure 7.1 shows how this looks graphically.
