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Theory and Modern Applications

Table 2 \(L^{2}\) errors and temporal convergence rates of Scheme II for Example 1

From: Analysis of two Legendre spectral approximations for the variable-coefficient fractional diffusion-wave equation

τ

γ = 1.1

γ = 1.5

γ = 1.9

Error

Order

Error

Order

Error

Order

1/10

1.3390e−03

6.9214e−03

9.3019e−03

1/20

3.5467e−04

1.9166

1.7767e−03

1.9619

2.3509e−03

1.9843

1/40

9.1195e−05

1.9595

4.4997e−04

1.9813

5.8999e−04

1.9944

1/80

2.3117e−05

1.9800

1.1321e−04

1.9908

1.4774e−04

1.9976

1/160

5.8191e−06

1.9901

2.8393e−05

1.9954

3.6962e−05

1.9989

1/320

1.4598e−06

1.9951

7.1094e−06

1.9977

9.2438e−06

1.9995