On a class of solvable difference equations generalizing an iteration process for calculating reciprocals
Abstract The well-known first-order nonlinear difference equation y n + 1 = 2 y n − x y n 2 , n ∈ N 0 , $$ y_{n+1}=2y_{n}-xy_{n}^{2}, \quad n\in {\mathbb {N}}_{0}, $$ naturally appeared in the problem of computing the reciprocal value of a given nonzero real number x. One of the interesting features...
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SpringerOpen
2021-04-01
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| Series: | Advances in Difference Equations |
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| Online Access: | https://doi.org/10.1186/s13662-021-03366-0 |
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doaj-c583eacf78be4137bcd37fd2e70e88412021-04-18T11:44:20ZengSpringerOpenAdvances in Difference Equations1687-18472021-04-012021111410.1186/s13662-021-03366-0On a class of solvable difference equations generalizing an iteration process for calculating reciprocalsStevo Stević0Mathematical Institute of the Serbian Academy of Sciences and ArtsAbstract The well-known first-order nonlinear difference equation y n + 1 = 2 y n − x y n 2 , n ∈ N 0 , $$ y_{n+1}=2y_{n}-xy_{n}^{2}, \quad n\in {\mathbb {N}}_{0}, $$ 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.https://doi.org/10.1186/s13662-021-03366-0Difference equationSolvable equationTheoretical solvabilityPractical solvabilityClosed-form formula |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Stevo Stević |
| spellingShingle |
Stevo Stević On a class of solvable difference equations generalizing an iteration process for calculating reciprocals Advances in Difference Equations Difference equation Solvable equation Theoretical solvability Practical solvability Closed-form formula |
| author_facet |
Stevo Stević |
| author_sort |
Stevo Stević |
| title |
On a class of solvable difference equations generalizing an iteration process for calculating reciprocals |
| title_short |
On a class of solvable difference equations generalizing an iteration process for calculating reciprocals |
| title_full |
On a class of solvable difference equations generalizing an iteration process for calculating reciprocals |
| title_fullStr |
On a class of solvable difference equations generalizing an iteration process for calculating reciprocals |
| title_full_unstemmed |
On a class of solvable difference equations generalizing an iteration process for calculating reciprocals |
| title_sort |
on a class of solvable difference equations generalizing an iteration process for calculating reciprocals |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1847 |
| publishDate |
2021-04-01 |
| description |
Abstract The well-known first-order nonlinear difference equation y n + 1 = 2 y n − x y n 2 , n ∈ N 0 , $$ y_{n+1}=2y_{n}-xy_{n}^{2}, \quad n\in {\mathbb {N}}_{0}, $$ 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. |
| topic |
Difference equation Solvable equation Theoretical solvability Practical solvability Closed-form formula |
| url |
https://doi.org/10.1186/s13662-021-03366-0 |
| work_keys_str_mv |
AT stevostevic onaclassofsolvabledifferenceequationsgeneralizinganiterationprocessforcalculatingreciprocals |
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