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Theory and Modern Applications

Table 11 Comparison of absolute errors for Example 5.2 with \(\pmb{\eta=2.5}\) and \(\pmb{\eta=5.0}\)

From: A new approach for one-dimensional sine-Gordon equation

τ

AE

RKM

η  = 2.5

AE

MHPM

η  = 2.5 [29]

AE

ADM

η  = 2.5 [29]

AE

RKM

η  = 5.0

AE

MHPM

η  = 5.0 [29]

AE

ADM

η  = 5.0 [29]

0.02

9.15E − 17

9.25104E − 8

9.25104E − 8

4.3E − 16

5.22002E − 11

5.22002E − 11

0.04

1.03E − 17

7.40084E − 7

7.40084E − 7

2.4E − 15

4.17602E − 10

4.17602E − 10

0.06

2.E − 17

2.49778E − 6

2.49778E − 6

3.9E − 15

1.40941E − 9

1.40941E − 9

0.08

1.07E − 16

5.92068E − 6

5.92068E − 6

9.1E − 16

3.34082E − 9

3.34082E − 9

0.1

2.16E − 16

1.15638E − 5

1.15638E − 5

5.3E − 15

6.52506E − 9

6.52506E − 9

0.3

2.9E − 16

3.12304E − 4

3.12304E − 4

1.8E − 14

1.76230E − 7

1.76230E − 7