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..
Shojaei, I., & Rahami, H. (2019). A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method. Journal of Algorithms and Computation, 51(1), 71-77. doi: 10.22059/jac.2019.71297
MLA
Iman Shojaei; Hossein Rahami. "A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method". Journal of Algorithms and Computation, 51, 1, 2019, 71-77. doi: 10.22059/jac.2019.71297
HARVARD
Shojaei, I., Rahami, H. (2019). 'A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method', Journal of Algorithms and Computation, 51(1), pp. 71-77. doi: 10.22059/jac.2019.71297
VANCOUVER
Shojaei, I., Rahami, H. A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method. Journal of Algorithms and Computation, 2019; 51(1): 71-77. doi: 10.22059/jac.2019.71297
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