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Numerical solution of two-point boundary-value problems


White, Andrew Benjamin (1974) Numerical solution of two-point boundary-value problems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/R9VN-9C49.


The approximation of two-point boundary-value problems by general finite difference schemes is treated. A necessary and sufficient condition for the stability of the linear discrete boundary-value problem is derived in terms of the associated discrete initial-value problem. Parallel shooting methods are shown to be equivalent to the discrete boundary-value problem. One-step difference schemes are considered in detail and a class of computationally efficient schemes of arbitrarily high order of accuracy is exhibited. Sufficient conditions are found to insure the convergence of discrete finite difference approximations to nonlinear boundary-value problems with isolated solutions. Newton's method is considered as a procedure for solving the resulting nonlinear algebraic equations. A new, efficient factorization scheme for block tridiagonal matrices is derived. The theory developed is applied to the numerical solution of plane Couette flow.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Keller, Herbert Bishop
Thesis Committee:
  • Unknown, Unknown
Defense Date:13 March 1974
Record Number:CaltechETD:etd-01312007-163410
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:421
Deposited By: Imported from ETD-db
Deposited On:31 Jan 2007
Last Modified:21 Dec 2019 04:36

Thesis Files

PDF (White_AB_1974.pdf) - Final Version
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