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Table 2 The coefficients of method (2.2) for order 5

From: G-stability one-leg hybrid methods for solving DAEs

k 4
\(\alpha _{n - 1}\) \(\frac{ - 288(48 + s(78 + s(36 + 5s))) + (1 + s)(8996 + 6055s+ 985s)\beta _{0}}{6(1660 + s(2265 + s(952 + 125s)))} \)
\(\alpha _{n - 2}\) \(\frac{72(24 + s(57 + s(32 + 5s))) - 3(1 + s)(1274 + s(913 + 155s)) \beta _{0}}{(3320 + 2s(2265 + s(952 + 125s)))} \)
\(\alpha _{n - 3}\) \(\frac{ - 32(8 + 5s)(2 + s(4 + s)) + 3(1 + s)(316 + s(281 + 55s)) \beta _{0}}{(3320 + 2s(2265 + s(952 + 125s)))} \)
\(\alpha _{n - 4}\) \(\frac{18(12 + s(33 + s(24 + 5s))) - (1 + s)(374 + s(367 + 85s))\beta _{0}}{6(1660 + s(2265 + s(952 + 125s)))} \)
\(\beta _{1}\) \(\frac{12(24 + 5s(4 + s)(5 + s(4 + s))) - 3(1 + s)(74 + s(96 + s(39 + 5s)))\beta _{0}}{s(1660 + s(2265 + s(952 + 125s)))} \)
\(\beta _{s}\) \(\frac{6( - 48 + 37\beta _{0})}{s(1660 + s(2265 + s(952 + 125s)))} \)