Table 4 Numerical errors and convergence orders in temporal direction with \(h=\frac{\pi }{300}\) and \(\beta =2\) at \(T=1\) for Example 2

α = 1/3

1/2

2.8602e-2

2.07

1/4

6.8097e-3

2.03

1/8

1.6620e-3

2.04

1/16

4.0529e-4

2.10

1/32

9.4220e-5

∗

α = 1/2

1/2

4.4594e-2

2.12

1/4

1.0231e-2

2.06

1/8

2.4506e-3

2.03

1/16

5.9844e-4

2.06

1/32

1.4358e-4

∗

α = 2/3

1/2

6.1011e-2

2.19

1/4

1.3382e-2

2.12

1/8

3.0810e-3

2.05

1/16

7.4636e-4

2.04

1/32

1.8138e-4

∗