Numerical Methods for Singularly Perturbed Differential Equations with Applications.

Abstract

During this period research was continued on the development and application of numerical methods for singularly-perturbed (or stiff) boundary value problems for ordinary differential equations and initial-boundary value problems for partial differential equations. The author concentrated most heavily on extensions to the adaptive finite element methods for partial differential equations. In particular, the stability of several mesh moving schemes was analyzed and local refinement techniques developed. The author also has some encouraging preliminary results on mesh moving methods in two dimensions. The investigators are applying their methods to several interesting physical problems, such as elastic-plastic solids, combustion, and a nonlinear Schrodinger equation which exhibits self focusing. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1984
Accession Number
ADA145639

Entities

People

  • J. E. Flaherty

Organizations

  • Rensselaer Polytechnic Institute

Tags

Communities of Interest

  • Advanced Electronics
  • Biomedical
  • Weapons Technologies

DTIC Thesaurus Topics

  • Air Force
  • Applied Mathematics
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Science
  • Differential Equations
  • Finite Element Analysis
  • Materials
  • Mathematics
  • New York
  • Partial Differential Equations
  • Phase Transformations
  • Schrodinger Equation
  • Shear Bands
  • Students
  • United States Military Academy

Fields of Study

  • Mathematics

Readers

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