Order conditions and symmetry for two-step hybrid methods

Authors: R. P. K. Chan; P. Leone; A. Tsai

Source: International Journal of Computer Mathematics, Volume 81, Number 12, December 2004 , pp. 1519-1536(18)

Publisher: Taylor and Francis Ltd

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Abstract:

In this study of two-step hybrid methods for second-order equations of the type y Prime

= f(y), we apply P-series [Hairer, E., Lubich, C. and Wanner, G. (2002). Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations. Springer Series in Computational Mathematics.] to formalise the approach of Chan [Chan, R. P. K. (2002). Two-step hybrid methods. Internal Publication.] to the order conditions, and present two characterizations of symmetry. Although order conditions can be obtained through the classical theory for the Nyström methods, it is of interest to derive particular simpler formulas for the class of two-step hybrid methods in order to facilitate the search for high-order methods. Moreover, the approach proves useful in analysing the symmetry of the hybrid methods.

Keywords: Two-step Hybrid Methods; Second-order Differential Equation; Order Conditions; Symmetry

Document Type: Research article

DOI: 10.1080/03057920412331272180

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