Preprint Article Version 1 This version is not peer-reviewed

On a Class of Hermite-Obrechkoff One-Step Methods with Continuous Spline Extension

Version 1 : Received: 23 May 2018 / Approved: 24 May 2018 / Online: 24 May 2018 (08:33:58 CEST)

A peer-reviewed article of this Preprint also exists.

Mazzia, F.; Sestini, A. On a Class of Conjugate Symplectic Hermite-Obreshkov One-Step Methods with Continuous Spline Extension. Axioms 2018, 7, 58. Mazzia, F.; Sestini, A. On a Class of Conjugate Symplectic Hermite-Obreshkov One-Step Methods with Continuous Spline Extension. Axioms 2018, 7, 58.

Journal reference: Axioms 2018, 7, 58
DOI: 10.3390/axioms7030058

Abstract

The class of A-stable symmetric one-step Hermite-Obrechkoff (HO) methods introduced in [1] for dealing with Initial Value Problems is analyzed. Such schemes have the peculiarity of admitting a multiple knot spline extension collocating the differential equation at the mesh points. As a new result, it is shown that these maximal order schemes are conjugate symplectic which is a benefit when the methods have to be applied to Hamiltonian problems. Furthermore a new efficient approach for the computation of the spline extension is introduced, adopting the same strategy developed in [2] for the BS linear multistep methods. The performances of the schemes are tested in particular on some Hamiltonian benchmarks and compared with those of the Gauss Runge-Kutta schemes and Euler-Maclaurin formulas of the same order.

Subject Areas

Initial Value Problems; One-step Methods; Hermite-Obrechkoff methods; symplecticity; B–Splines; BS Methods

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