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Questions tagged [difference-equations]

Difference equations, including linear and nonlinear equations, discrete version of topics in analysis, partial difference equations, oscillation theory, periodic solutions, almost periodic solutions, bifurcation theory, stability theory.

Difference equations, including linear and nonlinear equations, discrete version of topics in analysis, partial difference equations, oscillation theory, periodic solutions, almost periodic solutions, bifurcation theory, stability theory.

79 questions
6
votes
2 answers

Is there a solution/approximation for the non-linear difference equation $c_n = c_{n-1}+c_{\lceil \alpha n \rceil}$, where $0 < \alpha < 1$?

Is there a solution/approximation for the non-linear difference equation $c_n = c_{n-1}+c_{\lceil \alpha n \rceil}$, where $0 < \alpha < 1$?
Mike Schuster
  • 63
5
votes
2 answers

closed form solution of the following iterative equation?

is it possible to obtain a closed-form solution w.r.t. ${P_j:\forall j}$ (or in terms of special functions) for the following equations: $\alpha P_0=P_1$, $\alpha<1$ $\alpha P_j=P_{j+1}+P_{j+2}+\dots+P_{2j+1}$ for $j=1,2,....$ $\sum_{i=1}^\infty…
Michael Fan Zhang
  • 421
2
votes
2 answers

Discrete-analytic functions

I do not know if such concept already exists but lets consider functions which are equal to its Newton series. We know that functions which are equal to their Taylor series are called analytic, so lets call functions that are equal to their Newton…
Anixx
  • 9,302
2
votes
1 answer

Elementary proof of bounds on discrete derivative applied to $(1+n)^s$

I would like to show that for $s \in \mathbb{R}$ and a nonnegative integer $k$ $$ \triangle^k ((1+n)^s) \lesssim (1+|n|)^{s-k} $$ where $\triangle$ is the discrete derivative, i.e. $\triangle^1 ((1+n)^s) = (2+n)^s - (1+n)^s$. This is easy when $s…
Otis Chodosh
  • 7,077
2
votes
1 answer

how to solve this equation?

$Q=-{\frac {q \left( {{\rm e}^{{\it nb}\,{\it nv}\,\theta\,{\it Td}}}-1 \right) }{1-{{\rm e}^{\theta\,{\it Td}}}} \left( 1-{{\rm e}^{{\frac { Q\theta\,{\it Td}}{p}}}} \right) \left( 1-{{\rm e}^{{\frac {{\it nv} \,\theta\,Q{\it Td}}{p}}}} \right)…
sara
  • 21
0
votes
0 answers

A second order non-linear difference equations

I am trying to explicitly solve [ if possible and if the solution exists ] a second order non-linear difference equation of the form : $ a _ {n+2} ^2 + a_{n} ^2 + K = \lambda a_{n+1} $, where K and $\lambda$ are known positive constants ( assume…
Analysis Now
  • 1,451