Discretization vs. rounding error in Euler's method

The article of record as published may be located at http://dx.doi.org/10.4169/college.math.j.42.5.399Euler’s method for solving initial value problems is a good vehicle for observing the relationship between discretization error and rounding error in numerical computa- tion. As we reduce stepsize, in order to decrease discretization error, we necessarily increase the number of steps and introduce additional rounding error. The problem is common and can be quite troublesome. We will examine a simple device that can help delay the onset of this problem