A GENERALIZED METHOD FOR TREATING SINGULAR PERTURBATION PROBLEMS,

Abstract

Some of the existing methods of treating singular perturbation problems are studied, and a generalized method for solving such problems is developed. The generalized method was applied to a restricted three-body problem and to a general second-order linear ordinary differential equation with a turning point of arbitrary order. The results of the latter are used in obtaining the asymptotic expansions of the eigenvalues and eigenfunctions of a second-order linear equation with two turning points of arbitrary order. A special case of the eigenvalue problem is the Graetz problem. It arises in finding the temperature distribution of a fluid with constant properties having a parabolic velocity profile which enters suddenly into a round tube whose wall is kept at a different constant temperature. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1964
Accession Number
AD0606083

Entities

People

  • Ali Hasan Nayfeh

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Asymptotic Series
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Perturbations
  • Real Variables

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.