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:10.7907/81EDD440. https://resolver.caltech.edu/CaltechTHESIS:02082018101404674
Abstract
The asymptotic behavior, with respect to the large parameter µ, of two solutions of d^{2}y/dx^{2} + µ^{2} [c^{2}  x^{2} + 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 D_{v}(±√2µ t) with v = µ a^{2}/2  1/2 and t = Ø(x,µ^{1}). The function Ø(x,µ^{1}) and the quantity a^{2} 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.)) 

Subject Keywords:  (Mathematics and Physics) 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Minor Option:  Physics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 January 1952 
Record Number:  CaltechTHESIS:02082018101404674 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:02082018101404674 
DOI:  10.7907/81EDD440 
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:  16 May 2023 21:17 
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