Rational solutions of ordinary difference equations

doi:10.1016/j.jsc.2008.03.001

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	Rational solutions of ordinary difference equations
	Feng, Ruyong; Gao, Xiao-Shan; Huang, Zhenyu
	2008-10-01
发表期刊	JOURNAL OF SYMBOLIC COMPUTATION
ISSN	0747-7171
卷号	43 期号:10 页码:746-763
摘要	In this paper, we generalize the results of Feng and Gao [Feng, R., Gao, X.S., 2006. A polynomial time algorithm to find rational general solutions of first order autonomous ODEs. J. Symbolic Comput., 41(7), 735-762] to the case of difference equations. We construct two classes of ordinary difference equations (O Delta Es) whose solutions are exactly the univariate polynomial and rational functions respectively. On the basis of these O Delta Es and the difference characteristic set method, we give a criterion for an O Delta E with any order and nonconstant coefficients to have a rational type general solution. For the first-order autonomous (constant coefficient) O Delta E, we give a polynomial time algorithm for finding the polynomial solutions and an algorithm for finding the rational solutions for a given degree. (C) 2008 Elsevier Ltd. All rights reserved.
关键词	rational solution polynomial solution ordinary difference equation Puiseux series Laurent series
DOI	10.1016/j.jsc.2008.03.001
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Theory & Methods ; Mathematics, Applied
WOS记录号	WOS:000257517900004
出版者	ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6064
专题	系统科学研究所
通讯作者	Feng, Ruyong
作者单位	Acad Sinica, AMSS, Inst Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Feng, Ruyong,Gao, Xiao-Shan,Huang, Zhenyu. Rational solutions of ordinary difference equations[J]. JOURNAL OF SYMBOLIC COMPUTATION,2008,43(10):746-763.
APA	Feng, Ruyong,Gao, Xiao-Shan,&Huang, Zhenyu.(2008).Rational solutions of ordinary difference equations.JOURNAL OF SYMBOLIC COMPUTATION,43(10),746-763.
MLA	Feng, Ruyong,et al."Rational solutions of ordinary difference equations".JOURNAL OF SYMBOLIC COMPUTATION 43.10(2008):746-763.