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Theory and Modern Applications

Table 3 \(H^{1}\) errors and temporal convergence orders of Scheme I for Example 2

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

1.3114e−04

8.0296e−04

4.2595e−03

1/20

3.5169e−05

1.8987

2.8371e−04

1.5009

2.0039e−03

1.0879

1/40

9.4157e−06

1.9012

1.0026e−04

1.5006

9.3907e−04

1.0935

1/80

2.5159e−06

1.9040

3.5436e−05

1.5005

4.3911e−04

1.0967

1/160

6.6847e−07

1.9121

1.2522e−05

1.5008

2.0509e−04

1.0983

1/320

1.7832e−07

1.9064

4.4217e−06

1.5018

9.5731e−05

1.0992