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On modifications of Runge–Kutta–Nyström methods for solving y(4)=f(x,y)

I. Th Famelis
Ch Tsitouras
Journal / Anthology

Applied Mathematics and Computation
Year: 2016
Volume: 273
Issue: 15
Page range: 726-734

We present Runge–Kutta–Nyström type methods for the solution of a special fourth order initial value problem. Order conditions theory is given based on rooted trees. Thus a new set of SN-trees is introduced named ⊤4 and the enumeration of its elements is studied. A Mathematica package is also listed that may furnish instantly order conditions of very high orders. Finally a new 8th order method is constructed using Differential Evolution for solving the equations of condition. It outperforms by far the well-known established methods.

*Applied Mathematics

Enumeration of trees, Symbolic generation of trees, Order conditions, Differential Evolution