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Symbolic derivation of Runge–Kutta–Nyström type order conditions and methods for solving y  = f (x, y )

I. Th Famelis
Ch Tsitouras
Journal / Anthology

Applied Mathematics and Computation
Year: 2017
Volume: 297
Page range: 50-60

In this work we study the Runge–Kutta–Nyström (RKN) type methods for the solution of a special third order initial value problems. Based on rooted trees the relative order con- ditions theory is presented introducing a new set of SN-trees named  3 whose elements’ enumeration is given. A Mathematica package, that furnishes instantly order conditions of high orders, is also listed. Finally, a new method of order 8 is constructed that outperforms by far the methods found in the literature.

*Applied Mathematics