INVARIANT IMBEDDING AND THE ANALYSIS OF PROCESSES

Abstract

Many of the processes considered in modern physics and control theory lead, from the mathematical viewpoint, to nonlinear two-point boundary- value problems. These problems are difficult to treat computationally and analytically. A goal of the theory of invariant imbedding is to provide a systematic technique for converting these boundary-value problems into initial-value problems through use of appropriate variables and the employment of functional equation techniques. A particle multiplication process is considered for illustrative purposes. The classical equations and the invariant imbedding equations are derived and various interconnections are discussed. The paper is intended to be self-contained.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1963
Accession Number
AD0414523

Entities

People

  • Robert E. Kalaba

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Boundaries
  • Boundary Value Problems
  • Control Theory
  • Differential Equations
  • Dynamic Programming
  • Equations
  • Euler Equations
  • Formulas (Mathematics)
  • Integral Equations
  • Neutron Transport Theory
  • New York
  • Nonlinear Differential Equations
  • Partial Differential Equations
  • Physics
  • Radiative Transfer
  • United States

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra