Solution Strategies for Second Order, Nonlinear, One Dimensional, Two Point Boundary Value Problems by FEM Analysis

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.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1990
Accession Number
ADA246063

Entities

People

  • Baird S. Ritter

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Boundaries
  • Boundary Value Problems
  • Coast Guard
  • Computational Science
  • Coordinate Systems
  • Differential Equations
  • Engineering
  • Iterations
  • Linear Differential Equations
  • Linear Systems
  • Mechanical Engineering
  • Nonlinear Differential Equations
  • Nonlinear Systems
  • Numerical Analysis
  • Physics
  • Two Dimensional

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)