论文信息 - Symbolic derivation of Runge-Kutta-Nyström type order conditions and methods for solving y'''=f(x, y)

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

Abstract In this work we study the Runge–Kutta–Nystrom (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.

Ioannis Th. Famelis | Charalampos Tsitouras

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