# Correction to “On a Class of Hermite-Obreshkov One-Step Methods with Continuous Spline Extension” [Axioms 7(3), 58, 2018]

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## Introduction

**Theorem**

**1.**

**Proof.**

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Mazzia, F.; Sestini, A. On a class of conjugate symplectic Hermite-Obreshkov one-step methods with continuous spline extension. Axioms
**2018**, 7, 58. [Google Scholar] [CrossRef] - Hairer, E.; Lubich, C.; Wanner, G. Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd ed.; Springer: Berlin, Germany, 2006. [Google Scholar]
- Hairer, E.; Zbinden, C.J. On conjugate symplecticity of B-series integrators. IMA J. Numer. Anal.
**2013**, 33, 57–79. [Google Scholar] [CrossRef] - Iavernaro, F.; Mazzia, F.; Mukhametzhanov, M.; Sergeyev, Y. Conjugate symplecticity properties of Euler–Maclaurin methods and their implementation on the Infinity Computer. arXiv
**2018**, arXiv:1807.10952. [Google Scholar] - Hairer, E.; Murua, A.; Sanz-Serna, J. The non-existence of symplectic multi-derivative Runge–Kutta methods. BIT
**1994**, 34, 80–87. [Google Scholar] [CrossRef]

**Figure 1.**Kepler problem: results for the sixth (BSHO6, red dotted line) and eighth (BSHO8, purple dotted line) order BSHO methods, sixth order Euler–Maclaurin method (EMHO6, blue solid line) and sixth (Gauss–Runge–Kutta (GRK6), yellow dashed line) and eighth (GRK8-green dashed line) order Gauss methods. (

**Left**) error in the second component of the Lenz vector; (

**Right**) error in the first component of the Lenz vector.

**Figure 2.**Kepler problem: results for the sixth (BSHO6, red dotted line) and eighth (BSHO8, purple dotted line) order BSHO methods, sixth order Euler–Maclaurin method (EMHO6, blue solid line) and sixth (Gauss–Runge–Kutta (GRK6), yellow dashed line) and eighth (GRK8-green dashed line) order Gauss methods. (

**Top-left**) Absolute error of the numerical solution; (

**Top-right**) error in the Hamiltonian function; (

**Bottom-left**) error in the angular momentum; (

**Bottom-right**) error in the first component of the Lenz vector.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mazzia, F.; Sestini, A. Correction to “On a Class of Hermite-Obreshkov One-Step Methods with Continuous Spline Extension” [Axioms 7(3), 58, 2018]. *Axioms* **2019**, *8*, 59.
https://doi.org/10.3390/axioms8020059

**AMA Style**

Mazzia F, Sestini A. Correction to “On a Class of Hermite-Obreshkov One-Step Methods with Continuous Spline Extension” [Axioms 7(3), 58, 2018]. *Axioms*. 2019; 8(2):59.
https://doi.org/10.3390/axioms8020059

**Chicago/Turabian Style**

Mazzia, Francesca, and Alessandra Sestini. 2019. "Correction to “On a Class of Hermite-Obreshkov One-Step Methods with Continuous Spline Extension” [Axioms 7(3), 58, 2018]" *Axioms* 8, no. 2: 59.
https://doi.org/10.3390/axioms8020059