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

Ioannis Th. Famelis and Ch. Tsitouras

Applied Mathematics and Computation, 2017, vol. 297, issue C, 50-60

Abstract: 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 conditions 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.

Keywords: Enumeration of trees; Symbolic generation of trees; Order conditions; Differential evolution (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:297:y:2017:i:c:p:50-60

DOI: 10.1016/j.amc.2016.10.028

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