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