NUMERICAL SOLUTION OF NONLINEAR TWO-POINT BOUNDARY PROBLEMS by finite differences using newton'S METHOD.

Abstract

One method of solving nonlinear two-point boundary problems is to replace the nonlinear differential equations with implicit finite difference equations, linearize the nonlinear simultaneous algebraic equations, and solve them by an iterative process using Newton's well-known rule. This report describes this method in complete detail, gives a set of finite-difference equations for a general class of nonlinear two-point boundary problems, discusses the storage and solution of the band matrix, and suggests techniques for overcoming the difficulties of obtaining good initial guesses for the iterative procedure. Two examples are given to clarify the use of the method. The first example has multiple solutions, and both examples have boundary conditions specified at infinity. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1968
Accession Number
AD0676968

Entities

People

  • James F. Holt

Organizations

  • The Aerospace Corporation

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Difference Equations
  • Differential Equations
  • Equations
  • Linear Differential Equations
  • Mathematical Analysis
  • Nonlinear Differential Equations

Fields of Study

  • Mathematics

Readers

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