A Continuous Analogue of Sturm Sequences in the Context of Sturm-Liouville Equations. Revision.

Abstract

A shooting method is presented for finding the n sub th eigenvalue and eigenfunction of a Sturm-Liouville equation, in which the eigenvalue occurs nonlinearly. The method is verified in two ways: by applying the Sturm comparison and oscillation theorems to the continuous problem; and by applying Sturm sequences to a discretization. The method works for general (separated) boundary conditions, and provides an a-posteriori error estimate for the approximate eigenvalue. Analogues of the Sturm comparison, oscillation and separation theorems are proved for the discrete problem. A related method, which involves critical lengths in the invariant imbedding method, is shown to be incorrect for general boundary conditions.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1988
Accession Number
ADA195250

Entities

People

  • Ivo Babuška
  • L. Greenberg

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Analogs
  • Boundaries
  • Boundary Value Problems
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Liouville Equation
  • Maryland
  • Mathematics
  • Military Research
  • Oscillation
  • Physical Sciences
  • Sequences
  • Standards
  • Universities

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Materials Science and Engineering.