Theory and Modern Applications
Table 5 The maximum errors and convergence orders in spatial direction with \(\pmb{\tau =10^{-3}}\) and \(\pmb{t\in[0,0.05]}\)
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 ) | \(\boldsymbol {Rate_{h}}\) | |
\(\frac{ 1}{ 18}\) | 9.37861 × 10−4 | – | 2.14166 × 10−3 | – | 5.11973 × 10−3 | – |
\(\frac{ 1}{ 16}\) | 1.50810 × 10−3 | 4.03287 | 3.34524 × 10−3 | 3.78626 | 8.33874 × 10−3 | 4.14160 |
\(\frac{ 1}{ 14}\) | 2.55210 × 10−3 | 3.93964 | 5.72571 × 10−3 | 4.02473 | 1.45425 × 10−2 | 4.16504 |
\(\frac{ 1}{ 12}\) | 4.65456 × 10−3 | 3.89833 | 1.03879 × 10−2 | 3.86424 | 2.68133 × 10−2 | 3.96899 |
\(\frac{ 1}{ 10}\) | 9.42235 × 10−3 | 3.86810 | 2.11810 × 10−2 | 3.90773 | 5.31652 × 10−2 | 3.75439 |