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Theory and Modern Applications

Table 4 \(L^{2}\) errors and temporal convergence orders of Scheme II 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

9.9259e−05

4.2089e−04

5.3029e−04

1/20

2.5339e−05

1.9698

1.0644e−04

1.9834

1.3229e−04

2.0031

1/40

6.4011e−06

1.9850

2.6763e−05

1.9917

3.3056e−05

2.0007

1/80

1.6082e−06

1.9929

6.7107e−06

1.9957

8.2649e−06

1.9998

1/160

4.0289e−07

1.9970

1.6808e−06

1.9973

2.0665e−06

1.9998

1/320

1.0154e−07

1.9884

4.2141e−07

1.9959

5.1665e−07

1.9999