Chapter 9.1, Problem 21E

Answer the question “Why not?” that follows the three sentences after Example 2 on page 372.

TABLE 9.1.3 Improved Euler’s Method with h = 0.1

TABLE 9.1.4 Improved Euler’s Method with h = 0.05

A brief word of caution is in order here. We cannot compute all the values of $y_n^{*}$ first and then substitute these values into formula (3). In other words, we cannot use the data in Table 9.1.1 to help construct the values in Table 9.1.3. Why not?