On the asymptotic series solution of some higher order linear differential equations at turning points

The Lagrange manifold (WKB) formalism enables the determination of the asymptotic series solution of second-order wave type differential equations at turning points. The formalism also applies to higher order linear differential equations, as we make explicit here illustrating with some 4th order eq...

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Main Author:	Arthur D. Gorman
Format:	Article
Language:	English
Published:	Hindawi Limited 1984-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	higher order linear differential equations Lagrange manifold turning points WKB.
Online Access:	http://dx.doi.org/10.1155/S0161171284000600

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spelling	doaj-6e35318336094ddc87d8ca36f4d380f92020-11-24T23:25:28ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017354154810.1155/S0161171284000600On the asymptotic series solution of some higher order linear differential equations at turning pointsArthur D. Gorman0Department of Engineering Science, Lafayette College, Easton 18042, Pennsylvania, USAThe Lagrange manifold (WKB) formalism enables the determination of the asymptotic series solution of second-order wave type differential equations at turning points. The formalism also applies to higher order linear differential equations, as we make explicit here illustrating with some 4th order equations of physical significance.http://dx.doi.org/10.1155/S0161171284000600higher order linear differential equationsLagrange manifoldturning pointsWKB.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Arthur D. Gorman
spellingShingle	Arthur D. Gorman On the asymptotic series solution of some higher order linear differential equations at turning points International Journal of Mathematics and Mathematical Sciences higher order linear differential equations Lagrange manifold turning points WKB.
author_facet	Arthur D. Gorman
author_sort	Arthur D. Gorman
title	On the asymptotic series solution of some higher order linear differential equations at turning points
title_short	On the asymptotic series solution of some higher order linear differential equations at turning points
title_full	On the asymptotic series solution of some higher order linear differential equations at turning points
title_fullStr	On the asymptotic series solution of some higher order linear differential equations at turning points
title_full_unstemmed	On the asymptotic series solution of some higher order linear differential equations at turning points
title_sort	on the asymptotic series solution of some higher order linear differential equations at turning points
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1984-01-01
description	The Lagrange manifold (WKB) formalism enables the determination of the asymptotic series solution of second-order wave type differential equations at turning points. The formalism also applies to higher order linear differential equations, as we make explicit here illustrating with some 4th order equations of physical significance.
topic	higher order linear differential equations Lagrange manifold turning points WKB.
url	http://dx.doi.org/10.1155/S0161171284000600
work_keys_str_mv	AT arthurdgorman ontheasymptoticseriessolutionofsomehigherorderlineardifferentialequationsatturningpoints
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On the asymptotic series solution of some higher order linear differential equations at turning points

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