Theory and Modern Applications
Table 4 Numerical errors and convergent orders with \(\pmb{\lambda = 2}\) , \(\pmb{T= 1}\) , when \(\pmb{q = 4}\)
From: Numerical algorithms for the time-space tempered fractional Fokker-Planck equation
τ | α = 0.1 | α = 0.5 | α = 0.9 | |||
|---|---|---|---|---|---|---|
Err( τ ) | Rate | Err( τ ) | Rate | Err( τ ) | Rate | |
1/20 | 1.654609e−06 | * | 6.172450e−06 | * | 1.076598e−05 | * |
1/40 | 1.490310e−07 | 3.4728 | 4.637825e−07 | 3.7343 | 7.508511e−07 | 3.8418 |
1/80 | 1.286134e−08 | 3.5345 | 3.288428e−08 | 3.8180 | 4.965133e−08 | 3.9186 |
1/160 | 1.085597e−09 | 3.5665 | 2.255987e−09 | 3.8656 | 3.194957e−09 | 3.9580 |
1/320 | 9.059726e−11 | 3.5829 | 1.517684e−10 | 3.8938 | 2.027282e−10 | 3.9782 |