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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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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Abstract 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.
AbstractList 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.
Author Saad, Nasser
Ismail, Mourad E. H.
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Snippet We introduce a finite difference and q-difference analogues of the Asymptotic Iteration Method of Ciftci, Hall, and Saad. We give necessary, and sufficient...
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SubjectTerms Asymptotic iteration method
Asymptotic methods
Asymptotic properties
Difference equations
Finite difference method
polynomial solutions of difference equations
Polynomials
Primary 39A10
q-difference equations
Secondary33D99
Title A discrete and q asymptotic iteration method
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