Numerical Methods for Singularly Perturbed Differential Equations with Applications.

Abstract

During the period covered by this report the investigators continued their research on the development and application of adaptive numerical methods for singularly perturbed initial-boundary value problems for partial differential equations. They continued their analysis of the stability of mesh moving schemes for one-dimensional parabolic problems. Their also developed at moving mesh scheme with local refinement for two-dimensional hyperbolic systems and are considering a similar scheme for parabolic problems. They are applying our 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
Jun 01, 1985
Accession Number
ADA158969

Entities

People

  • J. E. Flaherty

Tags

Communities of Interest

  • Advanced Electronics
  • Weapons Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Boundary Value Problems
  • Computer Science
  • Differential Equations
  • Engineering
  • Equations
  • Finite Element Analysis
  • Mathematics
  • New York
  • Partial Differential Equations
  • Phase Transformations
  • Schrodinger Equation
  • Shear Bands
  • Students
  • United States
  • United States Military Academy

Fields of Study

  • Mathematics

Readers

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