Journal of Algorithms and Computation
Open Access

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

Document Type : Research Paper

Authors

Iman Shojaei 1
Hossein Rahami 2

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

https://doi.org/10.22059/jac.2019.71297
Abstract
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..

Keywords

diffusion equation
Finite Difference Method
convergence and stability
Journal of Algorithms and Computation
Volume 51, Issue 1
June 2019
Pages 71-77

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