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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. 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).
3. J. Nee and J. Duan, “Limit set of trajectories of the coupled viscous Burgers’ equations,” Appl. Math. Lett. 11(1), 57 (1998).
4. D. Kaya, “An explicit solution of coupled viscous Burgers’ equations by the decomposition method,” JJMMS 27(11), 675 (2001).
5. A. A. Soliman, “The modified extended tanh-function method for solving Burgers-type equations,” Physica A 361, 394 (2006).
6. S. E. Esipov, “Coupled Burgers’ equations: a model of polydispersive sedimentation,” Phys Rev E 52, 3711 (1995).
7. M. A. Abdou and A. A. Soliman, “Variational iteration method for solving Burgers and coupled Burgers equations,” J. Comput. Appl. Math. 181(2), 245251 (2005).
8. G. W. Wei and Y. Gu, “Conjugate filter approach for solving Burgers’ equation,” J. Comput. Appl. Math. 149(2), 439 (2002).
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).
10. M. Deghan, H. Asgar, and S. Mohammad, “The solution of coupled Burgers’ equations using Adomian-Pade technique,” Appl. Math. Comput. 189, 1034 (2007).
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).
12. R. C. Mittal and G. Arora, “Numerical solution of the coupled viscous Burgers’ equation,” Commun. Nonlinear Sci. Numer. Simulat. 16, 1304 (2011).
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).
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).
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).
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. 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. 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. 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).
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).
21. A. Bahadir, “A fully implicit finite-difference scheme for two-dimensional Burgers’ equation,” Appl. Math. Comp. 137, 131 (2003).
22. C. Fletcher, “Generating exact solutions of the two-dimensional Burgers’ equation,” Int. Numer. Meth. Fluids 3, 216 (1983).
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. 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).

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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.


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