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Theory and Modern Applications

Table 3 The results of different methods 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

MVIM

0.0

0.000000

0.000000

0.000000

0.000000

0.2

0.241977

0.240711

0.241965

0.241978

0.4

0.567812

0.563632

0.568115

0.567845

0.5

0.756014

0.749954

0.757564

0.756087

0.6

0.953566

0.945251

0.958259

0.953666

0.8

1.346364

1.332255

1.365240

1.346379

1.0

1.689498

1.668815

1.723810

1.686028