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

Abstract

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 p + r , where r = 2 and p 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 O ( h − r ) . 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.

Keywords

• initial value problems
• one-step methods
• Hermite–Obreshkov methods
• symplecticity
• B-splines
• BS methods