Asymptotic iteration method for solving Hahn difference equations.

IF 4.1 3区数学 Q1 Mathematics

Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-07-30 DOI:10.1186/s13662-021-03511-9

Lucas MacQuarrie, Nasser Saad, Md Shafiqul Islam

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引用次数: 2

Abstract

Hahn's difference operator $D_{q; w} f (x) = (f (q x + w) - f (x)) / ((q - 1) x + w)$ , $q \in (0, 1)$ , $w > 0$ , $x \neq w / (1 - q)$ is used to unify the recently established difference and q-asymptotic iteration methods (DAIM, qAIM). The technique is applied to solve the second-order linear Hahn difference equations. The necessary and sufficient conditions for polynomial solutions are derived and examined for the $(q; w)$ -hypergeometric equation.

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求解Hahn差分方程的渐近迭代法。

哈恩差分算子dq;用w f (x) = (f (q x + w) - f (x)) / ((q- 1) x + w)， q∈(0,1)，w > 0, x≠w / (1 - q)统一了最近建立的差分迭代法和q渐近迭代法(DAIM, qAIM)。将该方法应用于求解二阶线性哈恩差分方程。给出了多项式解的充分必要条件，并检验了(q;W) -超几何方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Difference Equations 数学-数学

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.