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Theory and Modern Applications

Table 2 Relative errors for Example 1, \(\alpha =1\)

From: A class of Runge–Kutta methods for nonlinear Volterra integral equations of the second kind with singular kernels

s

x (s)

NRK4

HPM

MIVM

0.0

0.000000

0.000000

0.000000

0.000000

0.2

0.197375

1.1146E−4

0.000000

0.000000

0.4

0.379949

2.7111E−4

1.3160E−5

7.8958E−6

0.5

0.462117

2.5751E−4

8.4394E−5

3.4623E−5

0.6

0.537050

1.1192E−4

3.5938E−4

1.8620E−6

0.8

0.664037

6.4304E−4

3.5103E−3

1.1099E−3

1.0

0.761594

2.0523E−3

2.0433E−2

5.8154E−3