Title of article :
A Closed-Form Solution for Two-Dimensional Diusion Equation Using Crank-Nicolson Finite Dierence Method
Author/Authors :
Shojaei, Iman Align Technology Inc - San Jose, USA , Rahami, Hossein School of Engineering Science - College of Engineering - University of Tehran, Tehran
Abstract :
In this paper a nite dierence method for solving
2-dimensional diusion equation is presented. The
method employs Crank-Nicolson scheme to improve -
nite dierence formulation and its convergence and sta-
bility. The obtained solution will be a recursive formula
in each step of which a system of linear equations should
be solved. Given the specic form of obtained matri-
ces, rather than solving the problem in each step using
conventional iterative methods, a closed-form solution is
formulated.
Keywords :
diffusion equation , nite difference method , con- vergence and stability
Journal title :
Astroparticle Physics
