Solution strategies for second order, nonlinear, one dimensional, two point boundary value problems by FEM analysis
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Authors
Ritter, Baird S.
Subjects
Galerkin FEM
nonlinear
quasilinearization
linearization
interpolation
iteration
differential equation
convergence
nonlinear
quasilinearization
linearization
interpolation
iteration
differential equation
convergence
Advisors
Salinas, David
Date of Issue
1990-12
Date
December 1990
Publisher
Monterey, California: Naval Postgraduate School
Language
Abstract
This research demonstrates the Galerkin FEM's ability to provide approximate solutions of second order, nonlinear, one dimensional, two point boundary value problems. The research concentrates on the development of linearization, iteration, and interpolation strategies for the solution of differential equations containing the nonlinear u2 term. Additionally, various numerical considerations are explored. Over 2000 cases were analyzed using various strategies and results detailing the efficacy of strategy combinations are presented. A linearization strategy known as quasilinearization consistently yielded excellent approximate solutions of the nonlinear differential equations investigated. It converged in a minimum number of iterations and was capable of solving equations which have large function order and activity over their specified domain.
Type
Thesis
Description
Series/Report No
Department
Mechanical Engineering
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funder
Format
xi, 165 p.
Citation
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.