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

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  • Famelis, Ioannis Th.
  • Tsitouras, Ch.

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.

Suggested Citation

  • Famelis, Ioannis Th. & Tsitouras, Ch., 2017. "Symbolic derivation of Runge–Kutta–Nyström type order conditions and methods for solving y′′′=f(x,y)," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 50-60.
    • Handle: RePEc:eee:apmaco:v:297:y:2017:i:c:p:50-60
    DOI: 10.1016/j.amc.2016.10.028
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    1. Famelis, I.Th. & Tsitouras, Ch., 2016. "On modifications of Runge–Kutta–Nyström methods for solving y(4)=f(x,y)," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 726-734.
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