Using Crank-Nicolson Numerical Method to solve Heat-Diffusion Problem
Article Sidebar
Main Article Content
Abstract
The current study aimed to use the Crank-Nicolson numerical method to solve Heat-Diffusion Problem in comparison with the ADI method. In this paper, the general formula of the Crank-Nicolson Numerical Method was derived and applied to solve the heat diffusion. The same problem then has been solved using ADI numerical method. The results of the Crank-Nicolson numerical method were compared with that of the ADI numerical method. The comparison results revealed that Crank-Nicolson is more accurate than the results of ADI at the initial steps of the problem solution.
Downloads
Article Details
Issue
Section
This work is licensed under a Creative Commons Attribution 4.0 International License.
Tikrit Journal of Pure Science is licensed under the Creative Commons Attribution 4.0 International License, which allows users to copy, create extracts, abstracts, and new works from the article, alter and revise the article, and make commercial use of the article (including reuse and/or resale of the article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made, and the licensor is not represented as endorsing the use made of the work. The authors hold the copyright for their published work on the Tikrit J. Pure Sci. website, while Tikrit J. Pure Sci. is responsible for appreciate citation of their work, which is released under CC-BY-4.0, enabling the unrestricted use, distribution, and reproduction of an article in any medium, provided that the original work is properly cited.
How to Cite
References
[1] A. Kaw and L. Snyder, “Introduction to scientific computing,” 2000.
[2] J. H. Mathews and K. D. Fink, Numerical methods using MATLAB, vol. 4. Pearson prentice hall Upper Saddle River, NJ, 2004.
[3] R. Mohammadi, “Exponential B-spline solution of convection-diffusion equations,” 2013.
[4] R. C. Mittal and R. Jain, “Redefined cubic B-splines collocation method for solving convection–diffusion equations,” Applied Mathematical Modelling, vol. 36, no. 11, pp. 5555–5573, 2012.
[5] M. Dehghan, “Weighted finite difference techniques for the one-dimensional advection–diffusion equation,” Applied Mathematics and Computation, vol. 147, no. 2, pp. 307–319, 2004.
[6] M. K. Kadalbajoo and P. Arora, “Taylor‐Galerkin B‐spline finite element method for the one‐dimensional advection‐diffusion equation,” Numerical Methods for Partial Differential Equations, vol. 26, no. 5, pp. 1206–1223, 2010.
[7] T. Cebeci, Convective heat transfer. Springer, 2002.
[8] W. Y. Yang et al., Applied numerical methods using MATLAB. John Wiley & Sons, 2020.
[9] B. Mebrate, “Numerical solution of a one dimensional heat equation with Dirichlet boundary conditions,” Am. J. Appl. Math, vol. 3, no. 6, pp. 305–311, 2015.
[10] T. Sauer, Numerical analysis. Addison-Wesley Publishing Company, 2011.
[11] V. Sigamani, J. J. H. Miller, R. Narasimhan, P. Mathiazhagan, and F. Victor, “Differential Equations and Numerical Analysis.” Springer, 2015.
[12] B. Sh. Mahmood, A. M. Gaftan, and F. A. Fawzi, “Alternating Directions Implicit Method for Solving Homogeneous Heat Diffusion Equation,” Ibn AL- Haitham Journal For Pure and Applied Sciences, vol. 33, no. 2, p. 62, Apr. 2020, doi: 10.30526/33.2.2427.
[13] S. Sathyapriya, G. Hamsavarthini, M. Meenakshi, and E. Tanushree, “A Study on Crank Nicolson Method for Solving Parabolic Partial Differential Equations,” 2021.
[14] S. A. Manna and B. J. Salem, “Numerical Analysis of the Burger Equation using Finite Differences,” AL-Rafidain Journal of Computer Sciences and Mathematics, vol. 4, no. 1, pp. 119–132, 2007.
[15] C. E. Abhulimen and B. J. Omowo, “Modified Crank-Nicolson Method for solving one dimensional Parabolic equations,” IOSR Journal of Mathematics, Volume15, no. 6, pp. 60–66, 2019.
[16] Bushra shakir mahmood, “Using the Theta Differences Method for solving the Bi-harmonic Equation,” thesis, University of Tikrit, iraq, 2019.
