Table 3 The \(L^{2}\) errors and temporal convergence order with different α and τ for Example 1, \(N=50\)

1/2

1.2653e − 04

–

2.6849e − 04

–

4.7402e − 04

–

1/4

3.1575e − 05

2.0027

6.7038e − 05

2.0018

1.1908e − 04

1.9930

1/8

7.8908e − 06

2.0005

1.6764e − 05

1.9996

2.9811e − 05

1.9981

1/16

1.9730e − 06

1.9998

4.2004e − 06

1.9968

7.4586e − 06

1.9989

1/32

4.9393e − 07

1.9980

1.0635e − 06

1.9818

1.8967e − 06

1.9754