Progress Report Number 2 on Contract AFOSR-84-0240.

Abstract

Implicit systems of differential equations of the form F(t,y,y') = 0 naturally arise in many circuit and control problems, economic models, and the solution of partial differential equations by the method of lines. Implicit systems are also called singular, differential-algebraic, semi-state, constrained, and descriptor. The theory is well understood, and numerical codes exist, for index zero, index one, and linear constant coefficient problems. Higher index systems occur in circuit and control problems. The numerical and analytic behavior of such higher index systems is not well understood and is incomplete. It has recently been shown that traditional methods, such as backward differences, need not work on higher index systems. Good characterizations of the solution manifold are often difficult to obtain. This research project is to study the numerical and analytic solution of higher index implicit differential equations. Applications will be made to circuit theory, control theory, and the analysis of numerically ill-conditioned index one systems.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1986
Accession Number
ADA172881

Entities

People

  • Stephen L. Campbell

Organizations

  • North Carolina State University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Air Force
  • Algebra
  • Applied Mathematics
  • Classification
  • Coefficients
  • Contracts
  • Control Theory
  • Differential Equations
  • Equations
  • Linear Algebra
  • Linear Systems
  • Mathematics
  • Nonlinear Differential Equations
  • North Carolina
  • Numerical Analysis
  • Partial Differential Equations
  • Universities

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra
  • Theoretical Analysis.