Table 4 1-D accuracy test: errors and convergence orders of 8th-order compact nonlinear scheme with Δt=0.3Δx²

1/5

5.154e-003

5.969e-003

8.959e-003

1/10

3.825e-004

3.75

4.392e-004

3.76

6.522e-004

3.78

1/20

7.963e-006

5.59

9.252e-006

5.57

1.588e-005

5.36

1/40

4.250e-008

7.55

6.042e-008

7.26

1.503e-007

6.72

1/80

1.339e-010

8.31

2.201e-010

8.10

7.984e-010

7.56

1/160

2.827e-013

8.89

3.801e-013

9.18

1.206e-012

9.37