About the expectation of the solution of the diffusion equation with random coefficients for the case of independent random processes

10.12737/5124 ◽  
2014 ◽  
Vol 2 (4) ◽  
pp. 100-103
Author(s):  
E. Korchagina ◽  
N. Andreeva ◽  
S. Sumera
Keyword(s):  
Diffusion Equation ◽  
Random Processes ◽  
Random Coefficients

K-L Expansion of a Random Process in Wavelet Bases

1998 ◽  
Author(s):  
Om P. Agrawal ◽  
Shantaram S. Pai
Keyword(s):  
Eigenvalue Problem ◽  
Wavelet Transforms ◽  
Series Representation ◽  
Numerical Algorithms ◽  
Analytical Techniques ◽  
Random Processes ◽  
Random Coefficients ◽  
Engineering Systems ◽  
Wavelet Bases ◽  
Orthogonal Wavelets

Abstract Random processes play a significant role in stochastic analysis of mechanical systems, structures, fluid mechanics, and other engineering systems. In this paper, a numerical method for series representation of random processes, with specified mean and correlation functions, in wavelet bases is presented. In this method, the Karhunen-Loeve expansion approach is used to represent a process as a linear sum of orthonormal eigenfunctions with uncorrelated random coefficients. The correlation and the eigenfunctions are approximated as truncated linear sums of compactly supported orthogonal wavelets. The eigenfunctions satisfy an integral eigenvalue problem. Using the above approximations, the integral eigenvalue problem is converted to a matrix (finite dimensional) eigenvalue problem. Numerical algorithms are discussed to compute one- and two-dimensional wavelet transforms of certain functions, and the resulting equations are solved to obtain the eigenvalues and the eigenfunctions. The scheme provides an improvement over other existing schemes. Two examples are considered to show the feasibility and effectiveness of this method. Numerical studies show that the results obtained using this method compare well with analytical techniques.

Classical random processes described by Schrödinger equation

2016 ◽  
Vol 14 (04) ◽  
pp. 1640006
Author(s):  
S. A. Rashkovskiy
Keyword(s):  
Schrödinger Equation ◽  
Diffusion Equation ◽  
Numerical Solution ◽  
Schrodinger Equation ◽  
Random Processes ◽  
Continuous Space ◽  
Classical Particles

It is shown that the Schrödinger equation can be written in the form of the diffusion equation for classical particles moving in a continuous space. A class of classical random processes described by the Schrödinger equation is considered. It is shown that such classical random processes can be used as a tool for the numerical solution of the Schrödinger equation.

Finding the moment functions of a solution of the two-dimensional diffusion equation with random coefficients

2010 ◽  
Vol 74 (6) ◽  
pp. 1127-1154
Author(s):  
Marina M Borovikova ◽  
Vladimir G Zadorozhnii
Keyword(s):  
Diffusion Equation ◽  
Random Coefficients ◽  
Two Dimensional ◽  
Dimensional Diffusion ◽  
Moment Functions ◽  
The Moment

scholarly journals N-ORDER MOMENT FUNCTION FOR THE SOLUTION OF THE CAUCHY PROBLEM FOR DIFFUSION EQUATION WITH RANDOM COEFFICIENTS

2017 ◽  
Vol 17 (8) ◽  
pp. 5-20
Author(s):  
T.V. Besedina
Keyword(s):  
Cauchy Problem ◽  
Diffusion Equation ◽  
Three Dimensional ◽  
Random Coefficients ◽  
Moment Function ◽  
Order Moment ◽  
Random Initial Condition ◽  
Initial Condition ◽  
Dimensional Diffusion ◽  
The Cauchy Problem

Formula for n-order moment function for the solution of the Cauchy problem for three-dimensional diffusion equation with random coefficients and random initial condition is derived.

Moment functions of a solution of the diffusion equation with Gaussian random coefficients

2010 ◽  
Vol 46 (7) ◽  
pp. 1068-1070
Author(s):  
M. M. Borovikova ◽  
V. G. Zadorozhniy
Keyword(s):  
Diffusion Equation ◽  
Random Coefficients ◽  
Moment Functions

A Method for Solving the Diffusion Equation with Random Coefficients

1991 ◽  
pp. 327-334 ◽  
Author(s):  
L. Carlomusto ◽  
A. Pianese ◽  
L. M. de Socio
Keyword(s):  
Diffusion Equation ◽  
Random Coefficients

Random Processes for Engineers

2015 ◽  
Author(s):  
Bruce Hajek
Keyword(s):  
Random Processes

The psychophysics of random processes

1976 ◽  
Author(s):  
Renwick E. Curry ◽  
T. Govindaraj
Keyword(s):  
Random Processes
Sign in / Sign up

Export Citation Format

Share Document