Theory and Modern Applications
Table 1 The maximum errors and convergence order in spatial direction with \(\pmb{\tau=10^{-3}}\)
h | α  = 0.9 | α  = 0.7 | α  = 0.5 | |||
|---|---|---|---|---|---|---|
e ( Ï„ , h ) | \(\boldsymbol {Rate_{h}}\) | e ( Ï„ , h ) | \(\boldsymbol {Rate_{h}}\) | e ( Ï„ , h ) | \(\boldsymbol {Rate_{h}}\) | |
\(\frac{ 1}{ 28}\) | 6.90559 × 10−5 | – | 7.52208 × 10−5 | – | 7.62869 × 10−5 | – |
\(\frac{ 1}{ 26}\) | 9.27939 × 10−5 | 3.98694 | 1.02720 × 10−4 | 4.20438 | 1.05053 × 10−4 | 4.31756 |
\(\frac{ 1}{ 24}\) | 1.28154 × 10−4 | 4.03352 | 1.40144 × 10−4 | 3.88122 | 1.40817 × 10−4 | 3.66048 |
\(\frac{ 1}{ 22}\) | 1.81614 × 10−4 | 4.00691 | 2.00611 × 10−4 | 4.12245 | 2.06562 × 10−4 | 4.40332 |
\(\frac{ 1}{ 20}\) | 2.65113 × 10−4 | 3.96890 | 2.92642 × 10−4 | 3.96161 | 3.03546 × 10−4 | 4.03874 |