Theory and Modern Applications
Table 2 Numerical errors and convergent orders with \(\pmb{\lambda = 2}\) , \(\pmb{T= 1}\) , when \(\pmb{q = 2}\)
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 | 8.679529e−05 | * | 4.906284e−04 | * | 1.069498e−03 | * |
1/40 | 2.252822e−05 | 1.9459 | 1.272612e−04 | 1.9468 | 2.772513e−04 | 1.9477 |
1/80 | 5.738671e−06 | 1.9729 | 3.241215e−05 | 1.9732 | 7.060275e−05 | 1.9734 |
1/160 | 1.448182e−06 | 1.9865 | 8.179024e−06 | 1.9865 | 1.781554e−05 | 1.9866 |
1/320 | 3.637467e−07 | 1.9932 | 2.054342e−06 | 1.9933 | 4.474725e−06 | 1.9933 |