TY - JOUR ID - 71297 TI - A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method JO - Journal of Algorithms and Computation JA - JAC LA - en SN - 2476-2776 AU - Shojaei, Iman AU - Rahami, Hossein AD - Department of Biomedical Engineering, University of Kentucky, Lexington, KY 40506, USA. AD - School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran Y1 - 2019 PY - 2019 VL - 51 IS - 1 SP - 71 EP - 77 KW - diffusion equation KW - Finite Difference Method KW - convergence and stability DO - 10.22059/jac.2019.71297 N2 - 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.. UR - https://jac.ut.ac.ir/article_71297.html L1 - https://jac.ut.ac.ir/article_71297_5397798f2c99c329aa87ce4d7a549428.pdf ER -