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Shojaei, Iman, Rahami, Hossein. (1398). A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method. , 51(1), 71-77. doi: 10.22059/jac.2019.71297
Iman Shojaei; Hossein Rahami. "A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method". , 51, 1, 1398, 71-77. doi: 10.22059/jac.2019.71297
Shojaei, Iman, Rahami, Hossein. (1398). 'A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method', , 51(1), pp. 71-77. doi: 10.22059/jac.2019.71297
Shojaei, Iman, Rahami, Hossein. A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method. , 1398; 51(1): 71-77. doi: 10.22059/jac.2019.71297

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

Journal of Algorithms and Computation
مقاله 6، دوره 51، شماره 1، شهریور 2019، صفحه 71-77    اصل مقاله (234.13 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22059/jac.2019.71297
نویسندگان
Iman Shojaei1؛ Hossein Rahami* 2
1Department of Biomedical Engineering, University of Kentucky, Lexington, KY 40506, USA.
2School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran
چکیده
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..
کلیدواژه‌ها
diffusion equation؛ Finite Difference Method؛ convergence and stability
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