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Erratum to “Extended RKN-type methods for numerical integration of perturbed oscillators” [Computer Physics Communications 180 (2009) 1777–1794]
Computer Physics Communications 181 (2010) 1658
Contents lists available at ScienceDirect
Computer Physics Communications www.elsevier.com/locate/cpc
Erratum
Erratum to “Extended RKN-type methods for numerical integration of perturbed oscillators” [Computer Physics Communications 180 (2009) 1777–1794] Xinyuan Wu State Key Laboratory for Novel Software at Nanjing University; Department of Mathematics, Nanjing University, Nanjing 210093, Nanjing 210097, P.R. China
a r t i c l e
i n f o
Article history: Received 29 May 2010 Accepted 5 June 2010 Available online 19 June 2010
On page 1780 in the original publication [1], the correct expression of (b) in Definition 3.1 should read: (b) If β τ1 ∈ BT, then B + b+ (β τ1 ) belongs to BT, where B + b+ is the operation that grafts the bottom vertex β τ1 to a new meagre vertex and then to a new fat black vertex (see β τb in Fig. 1). On page 1781 in the original publication [1], in Definition 3.4, F (∅)( y ) = 1 was written incorrectly. The correct expression should read p F (∅)( y ) = y. In Definition 3.6, the explanation of c i should be p
• c i where p is the number of fat black vertices and meagre vertices from ending vertices to the nearest fat white vertex i (or to the bottom vertex).
On page 1782 in the original publication [1], in the definition of
γ (β τ ) of Theorem 3.3,
k
should be changed into
k.
References [1] H.L. Yang, X.Y. Wu, Xiong You, Yonglei Fang, Extended RKN-type methods for numerical integration of perturbed oscillators, Comput. Phys. Comm. 180 (2009) 1777–1794.
DOI of original article: 10.1016/j.cpc.2009.05.010. E-mail address: [email protected]. 0010-4655/$ – see front matter doi:10.1016/j.cpc.2010.06.010
© 2009 Elsevier B.V.
All rights reserved.
Contents lists available at ScienceDirect
Computer Physics Communications www.elsevier.com/locate/cpc
Erratum
Erratum to “Extended RKN-type methods for numerical integration of perturbed oscillators” [Computer Physics Communications 180 (2009) 1777–1794] Xinyuan Wu State Key Laboratory for Novel Software at Nanjing University; Department of Mathematics, Nanjing University, Nanjing 210093, Nanjing 210097, P.R. China
a r t i c l e
i n f o
Article history: Received 29 May 2010 Accepted 5 June 2010 Available online 19 June 2010
On page 1780 in the original publication [1], the correct expression of (b) in Definition 3.1 should read: (b) If β τ1 ∈ BT, then B + b+ (β τ1 ) belongs to BT, where B + b+ is the operation that grafts the bottom vertex β τ1 to a new meagre vertex and then to a new fat black vertex (see β τb in Fig. 1). On page 1781 in the original publication [1], in Definition 3.4, F (∅)( y ) = 1 was written incorrectly. The correct expression should read p F (∅)( y ) = y. In Definition 3.6, the explanation of c i should be p
• c i where p is the number of fat black vertices and meagre vertices from ending vertices to the nearest fat white vertex i (or to the bottom vertex).
On page 1782 in the original publication [1], in the definition of
γ (β τ ) of Theorem 3.3,
k
should be changed into
k.
References [1] H.L. Yang, X.Y. Wu, Xiong You, Yonglei Fang, Extended RKN-type methods for numerical integration of perturbed oscillators, Comput. Phys. Comm. 180 (2009) 1777–1794.
DOI of original article: 10.1016/j.cpc.2009.05.010. E-mail address: [email protected]. 0010-4655/$ – see front matter doi:10.1016/j.cpc.2010.06.010
© 2009 Elsevier B.V.
All rights reserved.