期刊论文详细信息
Advances in Difference Equations | |
On a class of solvable difference equations generalizing an iteration process for calculating reciprocals | |
article | |
Stević, Stevo1  | |
[1] Mathematical Institute of the Serbian Academy of Sciences and Arts;Department of Medical Research, China Medical University Hospital, China Medical University | |
关键词: Difference equation; Solvable equation; Theoretical solvability; Practical solvability; Closed-form formula; | |
DOI : 10.1186/s13662-021-03366-0 | |
学科分类:航空航天科学 | |
来源: SpringerOpen | |
【 摘 要 】
The well-known first-order nonlinear difference equation$$ y_{n+1}=2y_{n}-xy_{n}^{2}, \quad n\in {\mathbb {N}}_{0}, $$ naturally appeared in the problem of computing the reciprocal value of a given nonzero real number x. One of the interesting features of the difference equation is that it is solvable in closed form. We show that there is a class of theoretically solvable higher-order nonlinear difference equations that include the equation. We also show that some of these equations are also practically solvable.
【 授权许可】
CC BY
【 预 览 】
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