The Modified Trapezoidal Rule for Computing Hypersingular Integral on Interval

Table 2

Errors of the mod-trapezoidal rule with 𝑠=𝑥_0𝑛−(1+𝜏)ℎ/2.

𝑛	𝜏=0	𝜏=2/3	𝜏=−2/3	𝜏=1/2
32	2.5227𝑒−002	2.9756𝑒−002	1.2230𝑒−001	−8.0605𝑒−002
64	1.1997𝑒−002	1.4808𝑒−002	6.0946𝑒−002	−4.1289𝑒−002
128	5.8224𝑒−003	7.3643𝑒−003	3.0401𝑒−002	−2.0913𝑒−002
256	2.8619𝑒−003	3.6669𝑒−003	1.5177𝑒−002	−1.0529𝑒−002
512	1.4173𝑒−003	1.8283𝑒−003	7.5815𝑒−003	−5.2839𝑒−003
1024	7.0490𝑒−004	9.1253𝑒−004	3.7886𝑒−003	−2.6471𝑒−003
ℎ^𝛼	1.0323	1.0054	1.0025	0.9857