Theory and Modern Applications
Table 8 Numerical errors and convergent orders with \(\pmb{\alpha = 0.5}\) , \(\pmb{\beta = 1.5}\) , \(\pmb{T = 1}\) , when \(\pmb{q = 4}\) , \(\pmb{\tau = h^{1/2}}\)
From: Numerical algorithms for the time-space tempered fractional Fokker-Planck equation
h | λ = 1 | λ = 3 | λ = 5 | |||
|---|---|---|---|---|---|---|
Err( h , τ ) | Rate | Err( h , τ ) | Rate | Err( h , τ ) | Rate | |
1/20 | 1.185249e−04 | * | 1.266770e−05 | * | 1.353897e−06 | * |
1/40 | 2.811036e−05 | 2.0760 | 3.072661e−06 | 2.0436 | 3.358635e−07 | 2.0112 |
1/80 | 5.483807e−06 | 2.3579 | 7.329619e−07 | 2.0677 | 9.796718e−08 | 1.7775 |
1/160 | 1.396193e−06 | 1.9737 | 1.787564e−07 | 2.0357 | 2.288642e−08 | 2.0978 |