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Theory and Modern Applications

Table 4 Relative errors for Example 2, \(\alpha =1\)

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

0.241977

5.2319E−3

4.9592E−5

4.1326E−6

0.4

0.567812

7.3616E−3

5.3363E−4

5.8118E−5

0.5

0.756014

8.0157E−3

2.0502E−3

9.6559E−5

0.6

0.953566

8.7199E−3

4.9215E−3

1.0487E−4

0.8

1.346364

1.0479E−2

1.4020E−2

1.1141E−5

1.0

1.689498

1.2242E−2

2.0309E−2

2.0539E−3