Next Article in Journal
An Alternative to Real Number Axioms
Next Article in Special Issue
Efficient Implementation of ADER Discontinuous Galerkin Schemes for a Scalable Hyperbolic PDE Engine
Previous Article in Journal
Single-Valued Neutrosophic Clustering Algorithm Based on Tsallis Entropy Maximization
Previous Article in Special Issue
A Convex Model for Edge-Histogram Specification with Applications to Edge-Preserving Smoothing
Article Menu

Export Article

Open AccessArticle
Axioms 2018, 7(3), 58; https://doi.org/10.3390/axioms7030058

On a Class of Conjugate Symplectic Hermite-Obreshkov One-Step Methods with Continuous Spline Extension

1
Dipartimento di Informatica, Università degli Studi di Bari Aldo Moro, 70125 Bari, Italy
2
Dipartimento di Matematica e Informatica U. Dini, Università di Firenze, 50134 Firenze, Italy
Member of the INdAM Research group GNCS.
*
Author to whom correspondence should be addressed.
Received: 23 May 2018 / Revised: 13 August 2018 / Accepted: 15 August 2018 / Published: 20 August 2018
(This article belongs to the Special Issue Advanced Numerical Methods in Applied Sciences)
Full-Text   |   PDF [860 KB, uploaded 20 August 2018]   |  

Abstract

The class of A-stable symmetric one-step Hermite–Obreshkov (HO) methods introduced by F. Loscalzo in 1968 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 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. View Full-Text
Keywords: initial value problems; one-step methods; Hermite–Obreshkov methods; symplecticity; B-splines; BS methods initial value problems; one-step methods; Hermite–Obreshkov methods; symplecticity; B-splines; BS methods
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top