Canonical forms and discrete Liouville–Green asymptotics for second-order linear difference equations

Canonical forms and discrete Liouville–Green asymptotics for second-order linear difference equations

Abstract Liouville–Green (WKB) asymptotic approximations are constructed for some classes of linear second-order difference equations. This is done starting from certain “canonical forms” for the three-term linear recurrence. Rigorous explicit bounds are established for the error terms in the asympt...

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Bibliographic Details
Main Author: Renato Spigler
Format: Article
Language:English
Published: SpringerOpen 2019-08-01
Series:Advances in Difference Equations
Subjects:
Difference equations
Canonical forms
Liouville–Green (WKB) asymptotics
Error bounds
Online Access:http://link.springer.com/article/10.1186/s13662-019-2293-z
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spelling doaj-c54b0ac253774bdea4ed764020d832e72020-11-25T03:54:03ZengSpringerOpenAdvances in Difference Equations1687-18472019-08-012019113210.1186/s13662-019-2293-zCanonical forms and discrete Liouville–Green asymptotics for second-order linear difference equationsRenato Spigler0Department of Mathematics and Physics, Roma Tre UniversityAbstract Liouville–Green (WKB) asymptotic approximations are constructed for some classes of linear second-order difference equations. This is done starting from certain “canonical forms” for the three-term linear recurrence. Rigorous explicit bounds are established for the error terms in the asymptotic approximations of recessive as well as dominant solutions. The asymptotics with respect to parameters affecting the equation is also discussed. Several illustrative examples are given.http://link.springer.com/article/10.1186/s13662-019-2293-zDifference equationsCanonical formsLiouville–Green (WKB) asymptoticsError bounds
collection DOAJ
language English
format Article
sources DOAJ
author Renato Spigler
spellingShingle Renato Spigler
Canonical forms and discrete Liouville–Green asymptotics for second-order linear difference equations
Advances in Difference Equations
Difference equations
Canonical forms
Liouville–Green (WKB) asymptotics
Error bounds
author_facet Renato Spigler
author_sort Renato Spigler
title Canonical forms and discrete Liouville–Green asymptotics for second-order linear difference equations
title_short Canonical forms and discrete Liouville–Green asymptotics for second-order linear difference equations
title_full Canonical forms and discrete Liouville–Green asymptotics for second-order linear difference equations
title_fullStr Canonical forms and discrete Liouville–Green asymptotics for second-order linear difference equations
title_full_unstemmed Canonical forms and discrete Liouville–Green asymptotics for second-order linear difference equations
title_sort canonical forms and discrete liouville–green asymptotics for second-order linear difference equations
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2019-08-01
description Abstract Liouville–Green (WKB) asymptotic approximations are constructed for some classes of linear second-order difference equations. This is done starting from certain “canonical forms” for the three-term linear recurrence. Rigorous explicit bounds are established for the error terms in the asymptotic approximations of recessive as well as dominant solutions. The asymptotics with respect to parameters affecting the equation is also discussed. Several illustrative examples are given.
topic Difference equations
Canonical forms
Liouville–Green (WKB) asymptotics
Error bounds
url http://link.springer.com/article/10.1186/s13662-019-2293-z
work_keys_str_mv AT renatospigler canonicalformsanddiscreteliouvillegreenasymptoticsforsecondorderlineardifferenceequations
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