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Table 3 The coefficients of method (2.2) for order 6

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

k 5
\(\alpha _{n - 1}\) \(\frac{( - 7200(120 + s(231 + s(142 + s(35 + 3s)))) + (1 + s)(615{,}436 + s(553{,}907 + 3s(53{,}483 + 5002s)))\beta _{0})}{(12(48{,}076 + s(77{,}175 + s(42{,}980 + 9975s+ 822s))))}\)
\(\alpha _{n - 2}\) \(\frac{ (300(120 + s(321 + s(236 + s(65 + 6s)))) - 4(1 + s)(17{,}929 + s(17{,}174 + s(5194 + 501s)))\beta _{0})}{(48{,}076 + s(77{,}175 + s(42{,}980 + 9975s+ 822s)))} \)
\(\alpha _{n - 3}\) \(\frac{ ( - 400(40 + s(117 + s(98 + 3s(10 + s)))) + 9(1 + s)(2948 + s(3325 + s(1127 + 118s)))\beta _{0})}{(48{,}076 + s(77{,}175 + s(42{,}980 + 9975s+ 822s)))} \)
\(\alpha _{n - 4}\) \(\frac{(225(60 + s(183 + s(164 + s(55 + 6s)))) - 4(1 + s)(5221 + s(6362 + 3s(794 + 91s)))\beta _{0}}{ (3(48{,}076 + s(77{,}175 + s(42{,}980 + 9975s+ 822s))))}\)
\(\alpha _{n - 5}\) \(\frac{( - 96(24 + s(75 + s(70 + s(25 + 3s)))) + (1 + s)(3436 + s(4379 + s(1753 + 222s))))\beta _{0}}{(4 (48{,}076 + s(77{,}175 + s(42{,}980 + 9975s+ 822s))))}\)
\(\beta _{1}\) \(\frac{(60(5 + 2s)(24 + s(5 + s)(20 + 3s(5 + s))) - 24(1 + s)(197 + s(302 + s(163 + s(37 + 3s))))\beta _{0})}{(s(48{,}076 + s(77{,}175 + s(42{,}980 + 9975s+ 822s))))}\)
\(\beta _{s}\) \(\frac{ - 7200 + 4728\beta _{0}}{ s(48{,}076 + s(77{,}175 + s(42{,}980 + 9975s+ 822s)))}\)