Let’s keep just the first two terms of the Taylor’s series: , where the To is the sum of all the terms we’re dropping—call it the truncation error. In what follows, we will have to distinguish between the correct or exact solution, x(t), and our approximate solution, xi. We hope.
With the Euler Method, our algorithm is [given to, x(to) = xo and f(x,t)]
example: , with to = 0 and xo = 4 and .
The algorithm is: .
The first few steps in the numerical solution are shown in the following table.
, where the To is the sum of all the terms we’re dropping—call it the truncation error. In what follows, we will have to distinguish between 
.
, with to = 0 and xo = 4 and 
.
.