SOME NEW TECHNIQUES IN THE DYNAMIC PROGRAMMING SOLUTION OF VARIATIONAL PROBLEMS

Abstract

It was seen that the numerical solution of a problem involving N state variables depended upon the computation of sequences of functions of N variables. This fact made the method routine only for the case where N = 1 or 2, with grave difficulties arising in the general case. In the paper, it is indicated how to overcome this difficulty for a large class of problems in which the underlying equations and the criterion function are linear, although the restraints on the forcing functions may be nonlinear, corresponding say to energy considerations. Finally, it is briefly indicated how the method of successive approximations may be combined with the foregoing techniques to reduce general variational problems, in which the equations and criterion function are nonlinear, to sequences of problems which can be solved numerically by means of sequences of functions of one variable.

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Document Details

Document Type
Technical Report
Publication Date
Aug 06, 1957
Accession Number
AD0606463

Entities

People

  • Richard E. Bellman

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Applied Mathematics
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Computer Programming
  • Difference Equations
  • Differential Equations
  • Digital Computers
  • Dynamic Programming
  • Equations
  • Euler Equations
  • Formulas (Mathematics)
  • Linear Differential Equations
  • Linear Systems
  • Nonlinear Differential Equations
  • Partial Differential Equations
  • Sequences

Fields of Study

  • Mathematics

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