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Theory and Modern Applications

Table 3 \(L^{\infty }\)-norm errors and convergence orders of Ũ obtained by the fourth-order scheme for Example 2

From: A fourth-order linearized difference scheme for the coupled space fractional Ginzburg–Landau equation

τ

h

α = 1.2

α = 1.5

α = 1.8

α = 2.0

\( \Vert u^{n}-\widetilde{U}^{n} \Vert _{\infty }\)

Order

\(\Vert u^{n}-\widetilde{U}^{n} \Vert _{\infty }\)

Order

\(\Vert u^{n}-\widetilde{U}^{n} \Vert _{\infty }\)

Order

\(\Vert u^{n}-\widetilde{U}^{n} \Vert _{\infty }\)

Order

1/8

1/8

5.65e−02

2.22e−02

2.58e−02

2.15e−02

1/16

1/16

8.41e−03

2.75

3.32e−03

2.74

2.17e−03

3.57

1.46e−03

3.88

1/32

1/32

7.56e−04

3.47

2.86e−04

3.54

1.43e−04

3.92

9.45e−05

3.95

1/64

1/64

5.35e−05

3.82

1.93e−05

3.89

9.18e−06

3.96

6.11e−06

3.95