IJPAM: Volume 14, No. 1 (2004)

A NOTE CONCERNING A DISCRETE TWO
DIMENSIONAL DIFFUSION PROBLEM
AND RANDOM WALKS

Richard Avery$^1$, Glenn Berman$^2$
$^{1,2}$College of Art and Sciences
Dakota State University
820 North Washington Ave.
Madison, South Dakota 57042-1799, USA
$^1$e-mail: rich.avery@dsu.edu
$^2$e-mail: glenn.berman@dsu.edu


Abstract.We find the solution of the partial difference equation

\begin{displaymath}\Delta_{t}v(x,y,t) = -r\nabla_x v(x,y,t) + l\Delta_x v(x,y,t)+ u \Delta_y v(x,y,t) - d \nabla_y v(x,y,t),\end{displaymath}

with initial condition $v(x,y,0)= f(x,y)$, which corresponds to the discrete two dimensional diffusion equation, by using a Green's function determined through a random walk.

Received: April 19, 2004

AMS Subject Classification: 39A12, 37H10

Key Words and Phrases: partial difference equations, Green's function, random walks

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 14
Issue: 1