Approximation of Solutions to Nonautonomous Difference Equations

Janusz Migda; Malgorzata Migda

doi:10.2478/tmmp-2018-0010

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Approximation of Solutions to Nonautonomous Difference Equations

Tatra Mountains Mathematical Publications

Volume 71 (2018): Issue 1 (December 2018)

By: Janusz Migda and Malgorzata Migda

Open Access

|Jan 2019

Abstract

We study the asymptotic properties of solutions to nonautonomous difference equations of the form

$Δ^{m} x_{n} = a_{n} f (n, x_{σ (n)}) + b_{n}, f : 𝕅 \times 𝕉 \to 𝕉, σ : 𝕅 \to 𝕅$ $${\Delta ^m}{x_n} = {a_n}f(n,{x_{\sigma (n)}}) + {b_n},\,\,f:N \times {\Bbb R} \to {\Bbb R},\,\,\sigma :{\Bbb N} \to {\Bbb N}$$

Using the iterated remainder operator and asymptotic difference pairs we establish some results concerning approximative solutions and approximations of solutions. Our approach allows us to control the degree of approximation.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2018-0010 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 109 - 121

Submitted on: Dec 11, 2017

Published on: Jan 25, 2019

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

nonautonomous equation,

difference pair,

prescribed asymptotic behavior,

asymptotically polynomial solution,

bounded solution

Related subjects:

Mathematics,

General mathematics

© 2019 Janusz Migda, Malgorzata Migda, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 71 (2018): Issue 1 (December 2018)