Table 2 Comparisons for solving Example 1 by different methods with \(\alpha =1.4, \ 1.5\) and 1.8 at \(t=1\)

64

0.129

3.7873e−4

69.6

0.101

3.7873e–4

63.6

0.103

3.7873e–4

63.7

128

1.038

1.9163e–4

163.1

0.632

1.9163e−4

144.0

0.646

1.9163e−4

143.7

256

4.828

9.6389e−5

272.0

3.963

9.6389e−5

354.0

3.898

9.6390e−5

338.7

512

28.391

4.8338e−5

375.8

25.382

4.8338e−5

590.5

23.993

4.8342e−5

546.4

1024

136.318

2.4205e−5

476.0

129.990

2.4206e−5

838.5

114.42

2.4212e−5

726.3

64

0.140

2.7756e−4

75.7

0.107

2.7756e−4

65.4

0.150

2.7756e−4

65.4

128

1.206

1.4046e−4

188.2

0.760

1.4046e−4

162.6

0.844

1.4046e−4

162.2

256

7.339

7.0658e−5

410.5

4.888

7.0654e−5

421.0

5.662

7.0654e−5

418.9

512

51.154

3.5436e−5

681.4

42.872

3.5435e−5

955.4

45.933

3.5439e−5

904.0

1024

289.79

1.7747e−5

1015.0

267.921

1.7744e−5

1657.2

277.638

1.7751e−5

1464.7

64

0.186

8.0708e−5

103.8

0.131

8.0708e−5

85.2

0.140

8.0708e−5

85.0

128

1.852

4.0979e−5

292.8

1.042

4.0979e−5

234.3

1.100

4.0978e−5

234.0

256

14.583

2.0659e−5

841.5

8.570

2.0659e−5

746.9

8.629

2.0659e−5

729.4

512

182.390

1.0375e−5

2472.5

96.153

1.0374e−5

2205.7

96.526

1.0374e−5

2164.3

1024

1708.245

5.2057e−6

6053.9

1075.756

5.1984e−6

6778.4

1058.220

5.1985e−6

6604.0