Authors: Stević, Stevo 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On a class of solvable difference equations generalizing an iteration process for calculating reciprocals
Journal: Advances in Difference Equations
Volume: 1
First page: Art. no. 205
Issue Date: 1-Dec-2021
Rank: ~M21a
ISSN: 1687-1847
DOI: 10.1186/s13662-021-03366-0
Abstract: 
The well-known first-order nonlinear difference equation yn+1=2yn−xyn2,n∈N0, 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.
Keywords: Closed-form formula | Difference equation | Practical solvability | Solvable equation | Theoretical solvability
Publisher: Springer Link

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