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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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-08-01
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| Series: | Advances in Difference Equations |
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| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2293-z |
| _version_ | 1818249378013380608 |
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| author | Renato Spigler |
| author_facet | Renato Spigler |
| author_sort | Renato Spigler |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-12T15:35:32Z |
| format | Article |
| id | doaj.art-c54b0ac253774bdea4ed764020d832e7 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-12T15:35:32Z |
| publishDate | 2019-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-c54b0ac253774bdea4ed764020d832e72022-12-22T00:20:01ZengSpringerOpenAdvances 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 |
| 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 |
| title | 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_short | 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 |
| 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 |