No data available.

Please log in to see this content.

You have no subscription access to this content.

No metrics data to plot.

The attempt to load metrics for this article has failed.

The attempt to plot a graph for these metrics has failed.

The full text of this article is not currently available.

oa

One-dimensional coupled Burgers’ equation and its numerical solution by an implicit logarithmic finite-difference method

http://aip.metastore.ingenta.com/content/aip/journal/adva/4/3/10.1063/1.4869637

false

Recommend This (0 Recommendations)

### Abstract

In this paper, an implicit logarithmic finite difference method (I-LFDM) is implemented for the numerical solution of one dimensional coupled nonlinear Burgers’ equation. The numerical scheme provides a system of nonlinear difference equations which we linearise using Newton's method. The obtained linear system via Newton's method is solved by Gauss elimination with partial pivoting algorithm. To illustrate the accuracy and reliability of the scheme, three numerical examples are described. The obtained numerical solutions are compared well with the exact solutions and those already available.

© 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.

Received 14 February 2014
Accepted 13 March 2014
Published online 24 March 2014

Article outline:

I. INTRODUCTION
II. NUMERICAL SCHEME (I-LFDM)
III. RESULTS AND DISCUSSIONS
IV. CONCLUSIONS

/content/aip/journal/adva/4/3/10.1063/1.4869637

1.

1. V. K. Srivastava, M. K. Awasthi, and M. Tamsir, “A fully implicit finite-difference solution to one dimensional coupled nonlinear Burgers’ equation,” Int. J. Math. Comp. Sci. Eng. 7(4), 283 (2013).

2.

2. V. K. Srivastava, M. K. Awasthi, M. Tamsir, and S. Singh, “An implicit finite-difference solution to one dimensional coupled Burgers’ equation,” Asian-European Journal of Mathematics 6(4), 1350058 (2013).

http://dx.doi.org/10.1142/S1793557113500587
4.

4. D. Kaya, “An explicit solution of coupled viscous Burgers’ equations by the decomposition method,” JJMMS 27(11), 675 (2001).

9.

9. A. H. Khater, R. S. Temsah, and M. M. Hassan, “A Chebyshev spectral collocation method for solving Burgers-type equations,” J. Comput. Appl. Math. 222(2), 333 (2008).

http://dx.doi.org/10.1016/j.cam.2007.11.007
11.

11. A. Rashid and A. I. B. Ismail, “A fourier Pseudospectral method for solving coupled viscous Burgers’ equations,” Comput. Methods Appl. Math. 9(4), 412 (2009).

http://dx.doi.org/10.2478/cmam-2009-0026
13.

13. R. Mokhtari, A. S. Toodar, and N. G. Chegini, “Application of the generalized differential quadrature method in solving Burgers’ equations,” Commun. Theor. Phys. 56(6), 1009 (2011).

http://dx.doi.org/10.1088/0253-6102/56/6/06
14.

14. V. K. Srivastava, S. Singh, and M. K. Awasthi, “Numerical solution of coupled Burgers’ equation by an implicit finite-difference scheme,” AIP Advances 3, 082131 (2013).

http://dx.doi.org/10.1063/1.4820355
15.

15. V. K. Srivastava, M. K. Awasthi, and S. Singh, “An implicit logarithmic finite-difference technique for two dimensional coupled viscous Burgers’ equation,” AIP Advances 3, 122105 (2013).

http://dx.doi.org/10.1063/1.4842595
16.

16. V. K. Srivastava and M. Tamsir, “Crank-Nicolson semi-implicit approach for numerical solutions of two-dimensional coupled nonlinear Burgers’ equations,” Int. J. Appl. Mech. Eng. 17(2), 571 (2012).

17.

17. V. K. Srivastava, M. Tamsir, U. Bhardwaj, and YVSS Sanyasiraju, “Crank-Nicolson scheme for numerical solutions of two-dimensional coupled Burgers’ equations,” IJSER 2(5), 44 (2011).

18.

18. M. Tamsir and V. K. Srivastava, “A semi-implicit scheme for numerical solutions of two-dimensional coupled Burgers’ equations,” IJSER 2(6), 46 (2011).

19.

19. R. Abazari and H. Borhanifar, “Numerical study of the solution of the Burgers and coupled Burgers equations by a differential transformation method,” Computers & Mathematics with Applications 59(8), 2711 (2010).

http://dx.doi.org/10.1016/j.camwa.2010.01.039
20.

20. R. C. Mittal and R. Jiwari, “Differential Quadrature Method for Numerical Solution of Coupled Viscous Burgers’ Equations,” Int. J. Comput. Methods Eng. Sci. Mech. 13(2), 88 (2012).

http://dx.doi.org/10.1080/15502287.2011.654175
22.

22. C. Fletcher, “Generating exact solutions of the two-dimensional Burgers’ equation,” Int. Numer. Meth. Fluids 3, 216 (1983).

23.

23. V. K. Srivastava, Ashutosh, and M. Tamsir, “Generating exact solution of three dimensional coupled unsteady nonlinear generalized viscous Burgers’ equations,” Int. J. Mod. Math. Sci. 5(1), 1 (2013).

24.

24. V. K. Srivastava and M. K. Awasthi, “(1 + n) - dimensional Burgers’ equation and its analytical solution: A comparative study of HPM, ADM and DTM,” Ain Shams Eng. J. (2013).

http://dx.doi.org/10.1016/j.asej.2013.10.004
http://aip.metastore.ingenta.com/content/aip/journal/adva/4/3/10.1063/1.4869637

Article metrics loading...

/content/aip/journal/adva/4/3/10.1063/1.4869637

2014-03-24

2016-10-27

### Abstract

In this paper, an implicit logarithmic finite difference method (I-LFDM) is implemented for the numerical solution of one dimensional coupled nonlinear Burgers’ equation. The numerical scheme provides a system of nonlinear difference equations which we linearise using Newton's method. The obtained linear system via Newton's method is solved by Gauss elimination with partial pivoting algorithm. To illustrate the accuracy and reliability of the scheme, three numerical examples are described. The obtained numerical solutions are compared well with the exact solutions and those already available.

Full text loading...

/deliver/fulltext/aip/journal/adva/4/3/1.4869637.html;jsessionid=dt0pIKlqU3-9yWT4zNjbeynE.x-aip-live-02?itemId=/content/aip/journal/adva/4/3/10.1063/1.4869637&mimeType=html&fmt=ahah&containerItemId=content/aip/journal/adva

###
Most read this month

Article

content/aip/journal/adva

Journal

5

3

true

true

## Comments