Theory and Modern Applications
Table 4 The maximum errors and convergence orders in spatial direction with \(\pmb{\tau=10^{-2}}\)
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 ) | \(\boldsymbol {Rate_{h}}\) | |
\(\frac{ 1}{ 28}\) | 7.49956 × 10−5 | – | 7.52514 × 10−5 | – | 7.68218 × 10−5 | – |
\(\frac{ 1}{ 26}\) | 9.95995 × 10−5 | 3.82860 | 1.02577 × 10−4 | 4.18013 | 1.03467 × 10−4 | 4.01801 |
\(\frac{ 1}{ 24}\) | 1.37506 × 10−4 | 4.02926 | 1.39977 × 10−4 | 3.88373 | 1.43168 × 10−4 | 4.05737 |
\(\frac{ 1}{ 22}\) | 2.01028 × 10−4 | 4.36463 | 1.97818 × 10−4 | 3.97498 | 2.12006 × 10−4 | 4.51202 |
\(\frac{ 1}{ 20}\) | 2.95158 × 10−4 | 4.02966 | 3.01869 × 10−4 | 4.43439 | 3.11013 × 10−4 | 4.02076 |