Methods for Solution of Stochastic Initial and Boundary Value Problems.

Abstract

Wave propagation in a one-dimensional random medium whose index of refraction is characterized randomly and is assumed to have small fluctuations about the mean was studied. The appropriate stochastic boundary value problem for the scattering region is transformed into a Cauchy type initial value problem for the boundary values of the random Green's function. The stochastic differential equation derived is a first order, nonlinear equation of the Riccati type. The initial value problem is solved in two ways: (1) by conventional power series perturbation expansion, and (2) by quasilinearization. In both cases the refracting medium are considered to be characterized by a general stationary process in the broad sense, and for such a process, general expressions for the statistical properties of the reflected and transmitted amplitude waves are derived.

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1974
Accession Number
ADA002080

Entities

People

  • Addi Ben-ghandor

Organizations

  • Tel Aviv University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Differential Equations
  • Equations
  • Partial Differential Equations
  • Power Series
  • Refraction
  • Refractive Index
  • Stationary Processes
  • Wave Propagation

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Statistical inference.
  • Wave Propagation and Nonlinear Chaotic Dynamics.