An effective collocation technique to solve the singular Fredholm integral equations with Cauchy kernel

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 2 Numerical results of Example 1 for Case (ii)

Node	y ( s )	\(\boldsymbol {y_{5}(s)}\)	\(\boldsymbol {\vert y(s)-y_{5}(s) \vert } \) for N = 4	\(\boldsymbol {\vert y(s)-y_{20}(s) \vert } \) [ 13 ]
−0.9	−0.634217	−0.634217	1.11022e − 16	−6.6613e − 16
−0.7	−0.876768	−0.876768	1.11022e − 16	7.49401e − 16
−0.5	−0.930368	−0.930368	1.11022e − 16	−5.5511e − 16
−0.3	−0.963476	−0.963476	2.22045e − 16	4.16334e − 16
−0.1	−1.044840	−1.044840	2.22045e − 16	−3.3307e − 16
0.0	−1.114080	−1.114080	2.22045e − 16	1.66533e − 16
0.1	−1.203830	−1.203830	0.00000e − 00	5.55112e − 16
0.3	−1.435350	−1.435350	2.22045e − 16	0.00000e − 00
0.5	−1.688440	−1.688440	0.00000e − 00	−7.7716e − 16
0.7	−1.828320	−1.828320	0.00000e − 00	0.00000e − 00
0.9	−1.460880	−1.460880	2.22045e − 16	9.43690e − 16