Hybrid Crank-Nicolson numerical method to solve Heat Diffusion problems
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Abstract
In this paper, we derive the hybrid Crank-Nicolson method based on the implicit method and the usual Crank-Nicolson method, where we get more accurate results and faster access to results. We also used Maple to implement the hybrid method and the results were identical
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References
[1] A. Kaw and L. Snyder, “Introduction to scientific computing,” 2000.
[2] 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.
[3] A. R. Mitchell and D. F. Griffiths, “The finite difference method in partial differential equations,” A Wiley-Interscience Publication, 1980.
[4] S. Sathyapriya, G. Hamsavarthini, M. Meenakshi, and E. Tanushree, “A Study on Crank Nicolson Method for Solving Parabolic Partial Differential Equations,” 2021.
[5] Q. Feng and B. Zheng, “Alternating Group Explicit-Implicit Method And Crank-Nicolson Method For Convection-Diffusion Equation,” 2009.
[6] K. Kakuda and N. Tosaka, “The generalized boundary element approach to Burgers’ equation,” Int J Numer Methods Eng, vol. 29, no. 2, pp. 245–261, 1990.
[7] T. Cebeci, Convective heat transfer. Springer, 2002.
[8] 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.
[9] D. J. Duffy, “A Critique of the Crank Nicolson Scheme Strengths and Weaknesses for Financial Instrument Pricing,” 2004.
[10] D. Britz and J. Strutwolf, “The Explicit Method,” 2016, pp. 89–100. doi: 10.1007/978-3-319-30292-8_5.
[11] Bushra shakir mahmood, “Using the Theta Differences Method for solving the Bi-harmonic Equation,” thesis, University of Tikrit, iraq, 2019.