Table 5 Error comparison at different time levels with parameters \((h, \Delta x)=(0.001,0.01)\) and \((\alpha _{1},\alpha _{2},\beta _{1},\beta _{2},\kappa _{0})=(2.0,2.0,0.2,0.8,-1.0)\) for u and v on \(\Omega =[-20,20]\)

1.0

1.34e–7

3.75e–8

40.109

1.34e–7

5.70e–8

21.290

2.29e–7

1.09e–7

21.392

2.83e–6

1.20e–6

19.923

2.0

1.41e–7

4.00e–8

79.928

1.40e–7

6.20e–8

42.555

3.16e–7

1.45e–7

43.115

4.04e–6

1.95e–6

39.938

3.0

1.49e–7

4.23e–8

120.273

1.46e–7

6.54e–8

63.541

4.03e–7

1.80e–7

64.403

5.33e–6

2.68e–6

59.636

5.0

1.64e–7

4.69e–8

199.060

1.57e–7

7.10e–8

100.729

5.82e–7

2.46e–7

107.506

8.05e–6

4.12e–6

99.475

7.0

1.78e–7

5.14e–8

278.519

1.69e–7

7.60e–8

147.976

7.61e–7

3.11e–7

148.760

1.09e–5

5.52e–6

138.652

9.0

1.93e–7

5.59e–8

358.730

1.80e–7

8.07e–8

191.171

9.41e–7

3.75e–7

192.853

1.37e–5

6.91e–6

179.023

1.0

2.32e–3

4.61e–4

39.790

2.29e–3

6.95e–4

21.367

4.72e–3

1.35e–3

26.467

1.64e–2

3.44e–3

20.147

2.0

2.83e–3

5.10e–4

79.383

2.82e–3

8.50e–4

42.610

7.78e–3

2.33e–3

53.094

2.93e–2

6.24e–3

39.745

3.0

3.34e–3

5.60e–4

123.809

3.34e–3

1.00e–3

64.103

1.17e–2

3.38e–3

79.825

4.21e–2

9.04e–3

60.158

5.0

4.36e–3

6.60e–4

200.306

4.40e–3

1.31e–3

102.442

1.97e–2

5.50e–3

132.757

6.76e–2

1.47e–2

99.885

7.0

5.37e–3

7.59e–4

274.728

5.44e–3

1.61e–3

145.512

2.76e–2

7.61e–3

185.927

9.25e–2

2.03e–2

140.867

9.0

6.39e–3

8.57e–4

362.107

6.49e–3

1.92e–3

191.648

3.56e–2

9.71e–3

192.787

1.17e–1

2.58e–2

178.660