Theory and Modern Applications
Table 3 The maximum errors and convergence orders 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 ) | \(\boldsymbol {Rate_{h}}\) | |
\(\frac{ 1}{ 28}\) | 6.91107 × 10−5 | – | 7.52059 × 10−5 | – | 7.63106 × 10−5 | – |
\(\frac{ 1}{ 26}\) | 9.28465 × 10−5 | 3.98390 | 1.02705 × 10−4 | 4.20514 | 1.03136 × 10−4 | 4.03963 |
\(\frac{ 1}{ 24}\) | 1.28210 × 10−4 | 4.03182 | 1.40131 × 10−4 | 3.88184 | 1.40804 × 10−4 | 4.40284 |
\(\frac{ 1}{ 22}\) | 1.81665 × 10−4 | 4.00520 | 2.00594 × 10−4 | 4.12254 | 2.06535 × 10−4 | 3.88945 |
\(\frac{ 1}{ 20}\) | 2.65168 × 10−4 | 3.96811 | 2.92628 × 10−4 | 3.96201 | 3.03532 × 10−4 | 4.06486 |