Numerical Methods for Singularly Perturbed Differential Equations with Applications.

Abstract

During the period covered by this report we continued our research 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. Results were obtained for collocation methods for vector systems of two-point boundary value problems and for adaptive grid finite element methods for partial differential equations. We are applying our methods to several interesting physical problems, such as, the deformation of nonlinear elastic beams and a nonlinear Schrodinger equation which exhibits self focusing. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1982
Accession Number
ADA121296

Entities

People

  • J. E. Flaherty

Organizations

  • Rensselaer Polytechnic Institute

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Air Force
  • Applied Mathematics
  • Boundary Layer
  • Boundary Value Problems
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Layers
  • Mathematics
  • New York
  • Numerical Analysis
  • Partial Differential Equations
  • Schrodinger Equation
  • Students
  • Universities
  • Wave Propagation
  • Waves

Fields of Study

  • Mathematics

Readers

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