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Theory and Modern Applications

Table 7 Numerical errors and convergent orders with \(\pmb{\alpha =0.5}\) , \(\pmb{\lambda = 2}\) , \(\pmb{T = 1}\) , when \(\pmb{q = 1}\) , \(\pmb{\tau = h^{2}}\)

From: Numerical algorithms for the time-space tempered fractional Fokker-Planck equation

h

β  = 1.1

β  = 1.5

β  = 1.9

Err( h , τ )

Rate

Err( h , τ )

Rate

Err( h , τ )

Rate

1/10

1.624398e−04

*

1.640323e−04

*

2.552445e−04

*

1/20

5.330786e−05

1.6075

3.880801e−05

2.0796

6.242922e−05

2.0316

1/40

1.371705e−05

1.9584

9.296651e−06

2.0616

1.532306e−05

2.0265

1/80

3.312170e−06

2.0501

2.244103e−06

2.0506

3.765450e−06

2.0248