Table 2 The maximum errors at time \(\pmb{t=1}\) and convergence orders in spatial and temporal directions with \(\pmb{h=\tau=\frac{1}{N+1}}\) for Example  2 with different α , and \(\pmb{\lambda=1.0}\) , the parameters \(\pmb{\gamma_{1}=0.7, 0.75, 0.80}\) , respectively, and \(\pmb{\gamma_{2}}\) and \(\pmb{\gamma _{3}}\) are selected in the set \(\pmb{S_{1}^{\alpha}(\gamma_{1},\gamma _{2},\gamma_{3})}\)

1.2

2⁶

1.1316e−06

-

1.3936e−06

-

1.6589e−06

-

2⁷

2.6235e−07

2.11

3.1707e−07

2.13

3.7199e−07

2.16

2⁸

6.3141e−08

2.05

7.5519e−08

2.07

8.7911e−08

2.08

2⁹

1.5497e−08

2.03

1.8440e−08

2.03

2.1384e−08

2.04

2¹⁰

3.8397e−09

2.01

4.5577e−09

2.02

5.2758e−09

2.02

1.5

2⁶

5.1105e−07

-

6.6675e−07

-

8.2269e−07

-

2⁷

1.2320e−07

2.05

1.7168e−07

1.96

2.2018e−07

1.90

2⁸

3.0239e−08

2.03

4.3597e−08

1.98

5.6957e−08

1.95

2⁹

7.4888e−09

2.01

1.0984e−08

1.99

1.4480e−08

1.98

2¹⁰

1.8633e−09

2.01

2.7567e−09

1.99

3.6502e−09

1.99

1.8

2⁶

3.7024e−07

-

1.0326e−07

-

1.7880e−07

-

2⁷

1.1190e−07

1.73

3.9593e−08

1.38

3.4713e−08

2.36

2⁸

3.0406e−08

1.88

1.1644e−08

1.77

7.5275e−09

2.21

2⁹

7.9086e−09

1.94

3.1315e−09

1.89

1.7469e−09

2.11

2¹⁰

2.0157e−09

1.97

8.1060e−10

1.95

4.2045e−10

2.05