A Survey of Some Applications of Probability and Stochastic Control Theory to Finite Difference Methods for Degenerate Elliptic and Parabolic Equations.

Abstract

Finite difference methods for degenerate linear and (certain) non-linear elliptic and parabolic equations are analyzed from a probabilistic point of view, and probabilistic methods to show convergence to the correct weak or strong sense solution. The techniques generalize results in numerical analysis, and the probabilistic approach allows some additional physical insight to be brought to bear on the problem of selecting suitable approximations and methods of solution. The equations which are discussed all have probabilistic interpretations.

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1974
Accession Number
ADA002983

Entities

People

  • Harold J. Kushner

Organizations

  • Brown University

Tags

DTIC Thesaurus Topics

  • Control Theory
  • Convergence
  • Equations
  • Mathematics
  • Numerical Analysis
  • Probability
  • Stochastic Control

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Operations Research
  • Theoretical Analysis.