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

Abstract

A closure of the Sturm sequence algorithm is found, leading to shooting method for the nth eigenvalue and eigenfunction of a Sturm-Liouville operator. The method works for general (separated) boundary conditions, and provides an a-posteriori error estimate for the approximate value of the nth eigenvalue. 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
Aug 01, 1986
Accession Number
ADA173404

Entities

People

  • I. Greenberg
  • Ivo Babuška

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Analogs
  • Boundaries
  • Boundary Value Problems
  • Difference Equations
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Formulas (Mathematics)
  • Liouville Equation
  • Maryland
  • Mathematics
  • Military Research
  • Physical Sciences
  • Sequences
  • Universities

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)