Citation
Fier, Jeffrey Michael (1985) Part I. Fold Continuation and the Flow Between Rotating, Coaxial Disks. Part II. Equilibrium Chaos. Part III. A Mesh Selection Algorithm for TwoPoint Boundary Value Problems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/cs9bft10. https://resolver.caltech.edu/CaltechETD:etd03262008150456
Abstract
Part I:
We consider folds in the solution surface of nonlinear equations with two free parameters. A system of equations whose solutions are fold paths is formulated and proved to be nonsingular in a neighborhood of a fold, thus making continuation possible. Efficient numerical algorithms employing block Gaussian elimination are developed for applying EulerNewton pseudoarclength continuation to the system, and these are shown to require fewer operations than other methods.
To demonstrate the use of these methods we calculate the flow between two infinite, rotating disks. For Reynold's number less than 1000, six separate solution sheets are found and completely described. Plots of 47 solutions for three values of the disk speed ratio and for Reynold's number equal to 625 are shown. These are compared with the solutions found by previous investigators.
Part II:
Two ordinary differential equations with parameters whose solution paths exhibit an infinite sequence of folds clustered about a limiting value are studied. Using phaseplane analysis, expressions for the limiting ratios of the parameter values at which these folds occur are derived and the limiting values are shown to be nonuniversal.
Part III:
A mesh selection algorithm for use in a code to solve firstorder nonlinear twopoint boundary value problems with separated end conditions is described. The method is based on equidistributing the global error of the box scheme, a numerical estimate of which is obtained from Richardson extrapolation. Details of the algorithm and examples of its performance on nonstiff and stiff problems are presented.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  Applied Mathematics  
Degree Grantor:  California Institute of Technology  
Division:  Engineering and Applied Science  
Major Option:  Applied Mathematics  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Thesis Committee: 
 
Defense Date:  10 December 1984  
Funders: 
 
Record Number:  CaltechETD:etd03262008150456  
Persistent URL:  https://resolver.caltech.edu/CaltechETD:etd03262008150456  
DOI:  10.7907/cs9bft10  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  1162  
Collection:  CaltechTHESIS  
Deposited By:  Imported from ETDdb  
Deposited On:  04 Apr 2008  
Last Modified:  19 Apr 2021 22:32 
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