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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