Table 2 The coefficients \(\{ \gamma_{K_{z},j}^{1} \}_{j=0}^{K_{z}}\) until \(K_{z} = 6\)
From: Multistep schemes for solving backward stochastic differential equations on GPU
\(K_{z}\) | \(\gamma_{K_{z},j}^{1}\) | ||||||
|---|---|---|---|---|---|---|---|
j = 0 | j = 1 | j = 2 | j = 3 | j = 4 | j = 5 | j = 6 | |
1 | \(\frac{1}{2}\) | \(\frac{1}{2}\) | |||||
2 | \(\frac{5}{12}\) | \(\frac{2}{3}\) | \(-\frac{1}{12}\) | ||||
3 | \(\frac{3}{8}\) | \(\frac{19}{24}\) | \(-\frac{5}{24}\) | \(\frac {1}{24}\) | |||
4 | \(\frac{35}{96}\) | \(\frac{5}{6}\) | \(-\frac{13}{48}\) | \(\frac {1}{12}\) | \(-\frac{1}{96}\) | ||
5 | \(\frac{131}{360}\) | \(\frac{151}{180}\) | \(-\frac{103}{360}\) | \(\frac{37}{360}\) | \(-\frac{1}{45}\) | \(\frac{1}{360}\) | |
6 | \(\frac{163}{448}\) | \(\frac{47}{56}\) | \(-\frac{129}{448}\) | \(\frac{3}{28}\) | \(-\frac{37}{1344}\) | \(\frac{1}{168}\) | \(-\frac {1}{1344}\) |