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Title

A fully implicit non-standard finite difference scheme for one dimensional Burgers' equation

Year: 1399
COI: JR_APRIE-7-3_007
Language: EnglishView: 49
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Authors

Abdolrahman Yaghoobi - Department of Applied Mathematics, Saravan Branch, Islamic Azad University, Saravan, Iran.
Hashem Saberi Najafi - Department of Applied Mathematics, Faculty of Mathematical Sciences, Guilan University, Rasht, Iran.

Abstract:

In this paper we have studied a numerical approximation to the solution of the nonlinear Burgers' equation. The presented scheme is obtained by using the Non-Standard Finite Difference Method (NSFD). The use of NSFD method and its approximations play an important role for the formation of stable numerical methods. The main advantage of the scheme is that the algorithm is very simple and very easy to implement.

Keywords:

Difference schemes, Burgers' equation, Non-Standard finite difference

Paper COI Code

This Paper COI Code is JR_APRIE-7-3_007. Also You can use the following address to link to this article. This link is permanent and is used as an article registration confirmation in the Civilica reference:

https://civilica.com/doc/1170101/

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Yaghoobi, Abdolrahman and Saberi Najafi, Hashem,1399,A fully implicit non-standard finite difference scheme for one dimensional Burgers' equation,https://civilica.com/doc/1170101

مراجع و منابع این Paper:

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  • [1]       Burgers, J. M. (1948). A mathematical model illustrating the ...
  • [2]       Bell, J. B. Colella, P. Glaz, H. M. (1989). ...
  • [3]       Burgers, J. M. (1974). The nonlinear diffusion equation. Reidel, ...
  • [4]       Ibragimov, N. H. (1994). CRC handbook of lie group ...
  • [5]       Polyanin, A. D. & Zaitsev, V. F. (2004). Handbook ...
  • [6]       Bluman, G. W. & Cole, J. D. (1969). The ...
  • [7]       Sugimoto, N. (1991). Burgers equation with a fractional derivative; ...
  • [8]       Whitham, G. B. (2011). Linear and nonlinear waves. John ...
  • [9]       Weinan, E., Khanin, K., Mazel, A., & Sinai, Y. ...
  • [10]   Bec, J., & Khanin, K. (2007). Burgers turbulence. Physics reports, 447(1-2), ...
  • [11]   Yaghoubi, A. R. & Najafi, H. S. (2015). Comparison ...
  • [12]   Najafi, H. S. & Yaghoubi, A. R. (2014). Solving ...
  • [13]   Yaghoubi, A. R. & Najafi, H. S. (2019). Non-standard ...
  • [14]   Mickens, R. E. (2005). Advances in the applications of ...
  • [15]   Mickens, R. E. (2001). A non-standard finite difference scheme ...
  • [16]   Mickens, R. E. (2003). A non-standard finite difference scheme ...
  • [17]   Mickens, R. E. (2005). A non-standard finite difference scheme ...
  • [18]   Mickens, R. E. (2007). Determination of denominator functions for ...
  • [19]   Mickens, R. E. (2006). Calculation of denominator functions for ...
  • 672-691. https://doi.org/10.1002/nu.20198 ...
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    Type of center: Azad University
    Paper count: 68
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