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Theory and Modern Applications

Table 4 Numerical results of Example 1 for Case (iv)

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

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

7.77156e − 16

−0.7

−0.876768

−0.876768

1.11022e − 16

2.22045e − 16

−0.5

−0.930368

−0.930368

1.11022e − 16

0.00000e − 00

−0.3

−0.963476

−0.963476

3.33067e − 16

−1.1102e − 16

−0.1

−1.044840

−1.044840

2.22045e − 16

−8.8818e − 16

0.0

−1.114080

−1.114080

2.22045e − 16

−4.4409e − 16

0.1

−1.203830

−1.203830

2.22045e − 16

0.00000e − 00

0.3

−1.435350

−1.435350

2.22045e − 16

0.00000e − 00

0.5

−1.688440

−1.688440

0.00000e − 00

−6.6613e − 16

0.7

−1.828320

−1.828320

0.00000e − 00

−2.2204e − 16

0.9

−1.460880

−1.460880

0.00000e − 00

1.11022e − 15