On a class of solvable difference equations generalizing an iteration process for calculating reciprocals

Advances in Difference Equations

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