Theory and Modern Applications
Table 1 Numerical errors and convergent orders with \(\pmb{\lambda = 2}\) , \(\pmb{T= 1}\) , when \(\pmb{q = 1}\)
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 | 1.042402e−03 | * | 5.951186e−03 | * | 1.211901e−02 | * |
1/40 | 5.228154e−04 | 0.9955 | 2.968097e−03 | 1.0036 | 5.998746e−03 | 1.0145 |
1/80 | 2.618102e−04 | 0.9978 | 1.482148e−03 | 1.0018 | 2.984155e−03 | 1.0073 |
1/160 | 1.310056e−04 | 0.9989 | 7.405955e−04 | 1.0009 | 1.488269e−03 | 1.0037 |
1/320 | 6.552793e−05 | 0.9994 | 3.701777e−04 | 1.0005 | 7.431822e−04 | 1.0018 |