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

I.Th. Famelis and Ch. Tsitouras

Applied Mathematics and Computation, 2016, vol. 273, issue C, 726-734

Abstract: 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.

Keywords: Enumeration of trees; Symbolic generation of trees; Order conditions; Differential Evolution (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:273:y:2016:i:c:p:726-734

DOI: 10.1016/j.amc.2015.10.024

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