Table 1 The coefficients \(\{ \gamma_{K_{y},j}^{K_{y}} \}_{j=0}^{K_{y}}\) until \(K_{y} = 6\)
From: Multistep schemes for solving backward stochastic differential equations on GPU
\(K_{y}\) | \(\gamma_{K_{y},j}^{K_{y}}\) | ||||||
|---|---|---|---|---|---|---|---|
j = 0 | j = 1 | j = 2 | j = 3 | j = 4 | j = 5 | j = 6 | |
1 | \(\frac{1}{2}\) | \(\frac{1}{2}\) | |||||
2 | \(\frac{1}{6}\) | \(\frac{2}{3}\) | \(\frac{1}{6}\) | ||||
3 | \(\frac{1}{8}\) | \(\frac{3}{8}\) | \(\frac{3}{8}\) | \(\frac{1}{8}\) | |||
4 | \(\frac{1}{12}\) | \(\frac{1}{3}\) | \(\frac{1}{6}\) | \(\frac{1}{3} \) | \(\frac{1}{12}\) | ||
5 | \(\frac{41}{600}\) | \(\frac{19}{75}\) | \(\frac{107}{600}\) | \(\frac {107}{600}\) | \(\frac{19}{75}\) | \(\frac{41}{600}\) | |
6 | \(\frac{19}{336}\) | \(\frac{3}{14}\) | \(\frac{15}{112}\) | \(\frac {4}{21}\) | \(\frac{15}{112}\) | \(\frac{3}{14}\) | \(\frac{19}{336}\) |