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  
Degree Grantor:  California Institute of Technology  
Division:  Physics, Mathematics and Astronomy  
Major Option:  Mathematics  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Thesis Committee: 
 
Defense Date:  1 January 1952  
Funders: 
 
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:  20 Dec 2019 19:45 
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