A Liouville--Green (or WKB) asymptotic approximation theory is developed for a class of almost--diagonal (''asymptotically diagonal'') linear second-order matrix difference equations. Rigorous and explicitly computable bounds for the error terms are obtained, the asymptotics being made with respect to both, the index and some parameter affecting the equation. The case of the associated inhomogeneous equations is also considered in detail. Some examples and a number of applications are presented for the purpose of illustration.

Cepale, M., & Spigler, R. (2017). Liouville-Green (WKB) asymptotics for almost-diagonal linear second-order matrix difference equations. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS [10.1080/10236198.2017.1361414].

Liouville-Green (WKB) asymptotics for almost-diagonal linear second-order matrix difference equations

CEPALE, MATTEO;SPIGLER, Renato
2017

Abstract

A Liouville--Green (or WKB) asymptotic approximation theory is developed for a class of almost--diagonal (''asymptotically diagonal'') linear second-order matrix difference equations. Rigorous and explicitly computable bounds for the error terms are obtained, the asymptotics being made with respect to both, the index and some parameter affecting the equation. The case of the associated inhomogeneous equations is also considered in detail. Some examples and a number of applications are presented for the purpose of illustration.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/323352
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