The Modified Trapezoidal Rule for Computing Hypersingular Integral on Interval

Table 4

A posteriori error estimate of the mod-trapezoidal rule.

𝑛	𝑠=1/4	ℎ^𝛼	𝑠=1/2	ℎ^𝛼	𝑠=5/8	ℎ^𝛼
32
64	−1.5814𝑒−003		−1.3849𝑒−003		−7.6112𝑒−004
128	−3.9776𝑒−004	1.9912	−3.5065𝑒−004	1.9817	−1.9765𝑒−004	1.9452
256	−9.9737𝑒−005	1.9957	−8.8202𝑒−005	1.9911	−5.0301𝑒−005	1.9743
512	−2.4971𝑒−005	1.9979	−2.2117𝑒−005	1.9956	−1.2684𝑒−005	1.9875
1024	−6.2473𝑒−006	1.9989	−5.5375𝑒−006	1.9978	−3.1846𝑒−006	1.9939