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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 4 The \(L^{2}\) errors and temporal convergence order with different τ for Example 2, \(\alpha=0.9\), \(N=50\)

From: Optimal error estimate of the Legendre spectral approximation for space-fractional reaction–advection–diffusion equation

τ

Error

Order

1/4

8.9062e − 04

–

1/8

2.2084e − 04

2.0118

1/16

5.5094e − 05

2.0031

1/32

1.3766e − 05

2.0008

1/64

3.4411e − 06

2.0002

1/20

3.9736e − 05

–

1/40

9.9305e − 06

2.0005

1/80

2.4824e − 06

2.0001

1/160

6.2059e − 07

2.0000

1/320

1.5515e − 07

2.0000

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