A Compact Tri-Colored Tree Theory for General ERKN Methods

Xinyuan Wu () and Bin Wang
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Xinyuan Wu: Nanjing University, Department of Mathematics
Bin Wang: Qufu Normal University, School of Mathematical Sciences

Chapter Chapter 8 in Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations, 2018, pp 193-220 from Springer

Abstract: 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.

Keywords: Redundant Trees; General Multi-frequency; Differential Element; General Oscillatory System; Rooted-tree Theory (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-9004-2_8

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DOI: 10.1007/978-981-10-9004-2_8

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