On a class of solvable difference equations generalizing an iteration process for calculating reciprocals
Keyword(s):
AbstractThe well-known first-order nonlinear difference equation $$ y_{n+1}=2y_{n}-xy_{n}^{2}, \quad n\in {\mathbb {N}}_{0}, $$ y n + 1 = 2 y n − x y n 2 , n ∈ 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.
2021 ◽
Vol 11
(1)
◽
pp. 68-74
Keyword(s):
1985 ◽
Vol 26
(4)
◽
pp. 430-451
◽
1980 ◽
Vol 22
(1)
◽
pp. 133-143
◽
2013 ◽
Vol 2013
◽
pp. 1-4
◽
Keyword(s):
2018 ◽
Vol 2018
◽
pp. 1-13
◽