Extended Error Expansion of Classical Midpoint Rectangle Rule for Cauchy Principal Value Integrals on an Interval

Table 1

Errors and convergence for the midpoint rectangle rule with .

32	6.2074e − 004	7.2296e − 004	2.6547e − 002	1.4010e − 002
64	1.6800e − 004	1.8082e − 004	3.6631e − 002	2.0390e − 002
128	4.3607e − 005	4.5210e − 005	4.2533e − 002	2.4147e − 002
256	1.1102e − 005	1.1303e − 005	4.5724e − 002	2.6186e − 002
512	2.8007e − 006	2.8257e − 006	4.7384e − 002	2.7249e − 002
1024	7.0330e − 007	7.0643e − 007	4.8230e − 002	2.7791e − 002
Convergence ratio	1.9571	1.9998	—	—