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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.


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
Major Option:Applied And Computational Mathematics
Thesis Committee:
  • Keller, Herbert Bishop (chair)
Defense Date:13 March 1974
Record Number: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:25 Dec 2012 14:59

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