A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method

Document Type : Research Paper


1 Department of Biomedical Engineering, University of Kentucky, Lexington, KY 40506, USA.

2 School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran


In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than solving the problem in each step using conventional iterative methods, a closed-form solution is formulated..