Citation
Owens, Robert Hunter (1952) An Asymptotic Study of a Glass of Ordinary Linear Differential Equations of the Second Order. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/81ED-D440. https://resolver.caltech.edu/CaltechTHESIS:02082018-101404674
Abstract
The asymptotic behavior, with respect to the large parameter µ, of two solutions of d2y/dx2 + µ2 [c2 - x2 + f(x, µ-1)] y = 0 is given where f(x, µ-1) = 0(µ-1) is subjected to suitable hypotheses and all variables are real. These solutions are approximated to by the parabolic cylinder functions Dv(±√2µ t) with v = µ a2/2 - 1/2 and t = Ø(x,µ-1). The function Ø(x,µ-1) and the quantity a2 are constructed as a part of the analysis in which the parameter µ is restricted in such a way that v is bounded away from the positive integers. The relative error of the approximating functions is uniform for all x.
Item Type: | Thesis (Dissertation (Ph.D.)) | ||||
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Subject Keywords: | Mathematics | ||||
Degree Grantor: | California Institute of Technology | ||||
Division: | Physics, Mathematics and Astronomy | ||||
Major Option: | Mathematics | ||||
Thesis Availability: | Public (worldwide access) | ||||
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Defense Date: | 1 January 1952 | ||||
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Record Number: | CaltechTHESIS:02082018-101404674 | ||||
Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:02082018-101404674 | ||||
DOI: | 10.7907/81ED-D440 | ||||
Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||
ID Code: | 10684 | ||||
Collection: | CaltechTHESIS | ||||
Deposited By: | Benjamin Perez | ||||
Deposited On: | 08 Feb 2018 18:42 | ||||
Last Modified: | 20 Dec 2019 19:45 |
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