Theory and Modern Applications
Table 6 The maximum errors and convergence orders in spatial direction with \(\pmb{\tau =10^{-4}}\) and \(\pmb{t\in[0,0.01]}\)
h | α  = 0.9 | α  = 0.8 | α  = 0.7 | |||
|---|---|---|---|---|---|---|
e ( Ï„ , h ) | \(\boldsymbol {Rate_{h}}\) | e ( Ï„ , h ) | \(\boldsymbol {Rate_{h}}\) | e ( Ï„ , h ) | \(\boldsymbol {Rate_{h}}\) | |
\(\frac{ 1}{ 18}\) | 1.44527 × 10−3 | – | 3.49475 × 10−3 | – | 5.11973 × 10−3 | – |
\(\frac{ 1}{ 16}\) | 2.39382 × 10−3 | 4.28410 | 5.47831 × 10−3 | 3.81663 | 8.51837 × 10−3 | 3.78163 |
\(\frac{ 1}{ 14}\) | 4.25691 × 10−3 | 4.31099 | 9.16482 × 10−3 | 3.85359 | 2.25842 × 10−2 | 3.96621 |
\(\frac{ 1}{ 12}\) | 7.87254 × 10−3 | 3.98855 | 1.71871 × 10−2 | 4.07904 | 4.42381 × 10−2 | 4.36155 |
\(\frac{ 1}{ 10}\) | 1.60094 × 10−2 | 3.89308 | 3.79037 × 10−2 | 4.33788 | 8.84836 × 10−2 | 3.80224 |