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Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations pp 193–220Cite as

A Compact Tri-Colored Tree Theory for General ERKN Methods

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Abstract

This chapter develops a compact tri-colored rooted-tree theory for the order conditions for general ERKN methods. The bottleneck of the original tri-colored rooted-tree theory is the existence of numerous redundant trees. This chapter first introduces the extended elementary differential mappings. Then, the new compact tri-colored rooted tree theory is established based on a subset of the original tri-colored rooted-tree set. This new theory makes all redundant trees no longer appear, and hence the order conditions of ERKN methods for general multi-frequency and multidimensional second-order oscillatory systems are greatly simplified.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, Jiangsu, China

    Xinyuan Wu

  2. School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, China

    Xinyuan Wu & Bin Wang

Authors
  1. Xinyuan Wu
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  2. Bin Wang
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Correspondence to Xinyuan Wu .

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Wu, X., Wang, B. (2018). A Compact Tri-Colored Tree Theory for General ERKN Methods. In: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations. Springer, Singapore. https://doi.org/10.1007/978-981-10-9004-2_8

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