A discrete and q asymptotic iteration method

We introduce a finite difference and q-difference analogues of the Asymptotic Iteration Method of Ciftci, Hall, and Saad. We give necessary, and sufficient condition for the existence of a polynomial solution to a general linear second-order difference or q-difference equation subject to a 'ter...

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Bibliographic Details
Published inJournal of difference equations and applications Vol. 26; no. 4; pp. 488 - 509
Main Authors Ismail, Mourad E. H., Saad, Nasser
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.04.2020
Taylor & Francis Ltd
Subjects
Asymptotic iteration method
Asymptotic methods
Asymptotic properties
Difference equations
Finite difference method
polynomial solutions of difference equations
Polynomials
Primary 39A10
q-difference equations
Secondary33D99
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Summary:We introduce a finite difference and q-difference analogues of the Asymptotic Iteration Method of Ciftci, Hall, and Saad. We give necessary, and sufficient condition for the existence of a polynomial solution to a general linear second-order difference or q-difference equation subject to a 'terminating condition', which is precisely defined. When a difference or q-difference equation has a polynomial solution, we show how to find the second solution.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1023-6198
1563-5120
DOI:10.1080/10236198.2020.1748021