+ + ... +

The results are tabulated in Table 6.2, which also presents the errors and the ratios of the errors between successive interval sizes. The global error of the trapezoid rule is 0(h2 ). Thus, for successive interval halvings,

. E(h) 0(h2) 2 Ratlo=--=---=2 =4

E(hI2) 0(hI2)2 (6.32)

The results presented in Table 6.2 illustrate the second-order behavior of the trapezoid rule.

6.3.2 Simpson's 1/3 Rule Simpson's 113 rule is obtained by fitting a second-degree polynomial to three equally spaced discrete points, as illustrated in Figure 6.6. The upper limit of integration X2 corresponds to s = 2. Thus, Eg. (6.19) gives