On Multiple Solutions of Singularly Perturbed Systems in the Conditionally Stable Case.

Abstract

This paper seeks the asymptotic behavior of solutions to nonlinear singularly perturbed boundary value problems for ordinary differential equations. Presuming a Jacobian matrix has a fixed number of (strictly) stable and unstable eigenvalues, the limiting solution can often be obtained from a reduced problem. Boundary layer behavior will satisfy a conditionally stable system, and multiple solutions will often result. The asymptotic structure of solutions is helpful in developing numerical solution schemes, and is vital in various applications (including some optimal control problems). (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1980
Accession Number
ADA087049

Entities

People

  • Robert E. O'malley Jr.

Organizations

  • University of Arizona

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Asymptotic Series
  • Boundaries
  • Boundary Layer
  • Boundary Value Problems
  • Coefficients
  • Convergence
  • Delta Functions
  • Differential Equations
  • Eigenvalues
  • Equations
  • Formulas (Mathematics)
  • Layers
  • Linear Differential Equations
  • Linear Systems
  • Mathematics
  • Nonlinear Systems
  • Riccati Equation

Fields of Study

  • Mathematics

Readers

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