Numerical Integration of Differential Equations Occurring in Two-Point Boundary Value Problems.

Abstract

An accurate procedure is described for numerically solving two-point boundary value problems which contain growing solutions. The procedure involves the process of reducing the order of a differential equation when one solution is known. Two applications of the procedure are given, a fourth order differential equation with two growing solutions and a system of eighth order differential equations of motion for a hemispherical shell. In both examples before the procedure is started, the equations are rewritten as a system of first order differential equations. It was found that when solving two-point boundary value problems by the reduction of order method, first order differential equations were generally easier to work with than higher order differential equations. For both applications a computer program was developed to solve the system of differential equations. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1979
Accession Number
ADA065011

Entities

People

  • Arthur R. Robinson
  • Rodger B. Jackson

Organizations

  • University of Illinois Urbana–Champaign

Tags

Communities of Interest

  • Air Platforms
  • Ground and Sea Platforms
  • Space
  • Weapons Technologies

DTIC Thesaurus Topics

  • Air Force
  • Air Force Facilities
  • Boundary Value Problems
  • Capillary Electrophoresis
  • Civil Engineering
  • Computational Science
  • Coordinate Systems
  • Differential Equations
  • Eigenvalues
  • Engineering
  • Engineers
  • Equations
  • Equations Of Motion
  • Materials
  • Mechanical Engineering
  • Mechanics
  • Military Research

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Fluid Mechanics and Fluid Dynamics.
  • Systems Analysis and Design