Optimal third order SSP LMMs
steps | order | SSP coefficient | $\alpha_i$ | $\beta_i$ |
$m$ | $r$ | $c$ | |
4 | 3 | $ \frac{1}{3}$ | $ \frac{16}{27},0,0,\frac{11}{27}$ | $\frac{16}{9},0,0,\frac{4}{9}$ |
5 | 3 | $\frac{1}{2}$ | $\frac{25}{32},0,0,0, \frac{7}{32}$ | $\frac{25}{16},0,0,0,\frac{5}{16}$ |
6 | 3 | 0.5828 | 0.850708871672579,0,0,0,0.030664864534383,0.118626263793039 | 1.459638436015276,0,0,0,0.052614491749200,0.203537849338252 |
5 | 4 | 0.0212 | 0.048963857415019, 0, 0.008344481263315, 0.899467614699687 | 2.310657177904340, 0, 0.393785059937890, 2.039789323349077, 0 |
6 | 4 | 0.1648 |
0.342460855717007, 0, 0, 0.191798259434736, 0.093562124939008, 0.372178759909247 | 2.078553105578060, 0, 0, 1.164112222279710, 0.567871749748709, 0 |