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A Compact Tri-Colored Tree Theory for General ERKN Methods

In: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations

Author

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  • Xinyuan Wu

    (Nanjing University, Department of Mathematics
    Qufu Normal University, School of Mathematical Sciences)

  • Bin Wang

    (Qufu Normal University, School of Mathematical Sciences)

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.

Suggested Citation

  • Xinyuan Wu & Bin Wang, 2018. "A Compact Tri-Colored Tree Theory for General ERKN Methods," Springer Books, in: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations, chapter 0, pages 193-220, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-9004-2_8
    DOI: 10.1007/978-981-10-9004-2_8
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