Computational aspects of normal form expansions
作者:
Peter B. Kahn,
Diana Murray,
Yair Zarmi,
期刊:
AIP Conference Proceedings
(AIP Available online 1995)
卷期:
Volume 326,
issue 1
页码: 633-661
ISSN:0094-243X
年代: 1995
DOI:10.1063/1.47309
出版商: AIP
数据来源: AIP
摘要:
We use the method of normal forms (NF) to explore perturbative solutions to a broad class of nonlinear differential equations and to symplectic planar maps. The method employs introduction of a transformation from the original variables to a new set that yields equations that are more amenable to analysis. The transformation is not unique and ‘‘freedom’’ is thereby introduced, which is exploited to tailor the structure of the expansion to match various constraints that one might impose. Kahn and Zarmi, and Kahn, Murray, and Zarmi have introduced and used the method of minimal normal forms (MNF) and variations thereof that exploit the lack of uniqueness and consequent freedom of choice in the normal form expansion to realize ‘‘compact’’ expansions that have a simple structure, are easy to use, and have significant computational advantages over other schemes. © 1995American Institute of Physics
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