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

• Main Authors: Francesca Mazzia, Alessandra Sestini
• Format: Article
• Language: English
• Published: MDPI AG 2019-05-01
• Series: Axioms
• Subjects: initial value problems; one-step methods; Hermite–Obreshkov methods; symplecticity; B-splines; BS methods
• Online Access: https://www.mdpi.com/2075-1680/8/2/59
• ISSN: 2075-1680

The authors of the above mentioned paper specify that the considered class of one-step symmetric Hermite-Obreshkov methods satisfies the property of conjugate-symplecticity up to order <inline-formula> <math display="inline"> <semantics> <mrow> <mi>p</mi> <mo>+</mo> <mi>r</mi> <mspace width="0.166667em"></mspace> <mo>,</mo> </mrow> </semantics> </math> </inline-formula> where <inline-formula> <math display="inline"> <semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> and <i>p</i> is the order of the method. This generalization of conjugate-symplecticity states that the methods conserve quadratic first integrals and the Hamiltonian function over time intervals of length <inline-formula> <math display="inline"> <semantics> <mrow> <mi>O</mi> <mo>(</mo> <msup> <mi>h</mi> <mrow> <mo>&#8722;</mo> <mi>r</mi> </mrow> </msup> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>. Theorem 1 of the above mentioned paper is then replaced by a new one. All the other results in the paper do not change. Two new figures related to the already considered Kepler problem are also added.