The Modified Trapezoidal Rule for Computing Hypersingular Integral on Interval

Table 1

Errors of the mod-trapezoidal rule with 𝑠=𝑥_[0𝑛/4]+(1+𝜏)ℎ/2.

𝑛	𝜏=0	𝜏=2/3	𝜏=−2/3	𝜏=1/2
32	3.5392𝑒−002	−7.1780𝑒−004	1.1040𝑒−003	1.7473𝑒−002
64	1.6961𝑒−002	−1.9364𝑒−004	2.7065𝑒−004	8.4165𝑒−003
128	8.3004𝑒−003	−5.0195𝑒−005	6.6991𝑒−005	4.1332𝑒−003
256	4.1057𝑒−003	−1.2773𝑒−005	1.6664𝑒−005	2.0484𝑒−003
512	2.0417𝑒−003	−3.2214𝑒−006	4.1554𝑒−006	1.0198𝑒−003
1024	1.0181𝑒−003	−8.0885𝑒−007	1.0375𝑒−006	5.0878𝑒−004
ℎ^𝛼	1.0239	1.9587	2.0111	1.0204