[1] Burgers, J. M. (1948). A mathematical model illustrating the theory of turbulence. Advances in applied mechanics, 1, 171-199. https://doi.org/10.1016/S0065-2156(08)70100-5
[2] Bell, J. B. Colella, P. Glaz, H. M. (1989). A second-order projection method for the incompressible Navier-Stokes equations.
Journal of computational physics,
85, 257-283.
https://doi.org/10.1016/0021-9991(89)90151-4
[3] Burgers, J. M. (1974). The nonlinear diffusion equation. Reidel, Dordrecht.
[4] Ibragimov, N. H. (1994). CRC handbook of lie group analysis of differential equations, Vol. 1, symmetries, exact solutions and conservation laws. CRC Press, Boca Raton.
[5] Polyanin, A. D. & Zaitsev, V. F. (2004). Handbook of nonlinear partial differential equations. Chapman & Hall/CRC, Boca Raton.
[6] Bluman, G. W. & Cole, J. D. (1969). The general similarity solution of the heat equation. Journal of mathematics and mechanics, 18, 1025-1042. https://www.jstor.org/stable/24893142
[7] Sugimoto, N. (1991). Burgers equation with a fractional derivative; hereditary effects on nonlinear acoustic waves. Journal of fluid mechanics, 225, 631-653.
[8] Whitham, G. B. (2011). Linear and nonlinear waves. John Wiley & Sons.
[9] Weinan, E., Khanin, K., Mazel, A., & Sinai, Y. (2000). Invariant measures for Burgers equation with stochastic forcing. Annals of mathematics, 151(3), 877-960. https://doi.org/10.2307/121126
[10] Bec, J., & Khanin, K. (2007). Burgers turbulence. Physics reports, 447(1-2), 1-66.
[11] Yaghoubi, A. R. & Najafi, H. S. (2015). Comparison between standard and non-standard finite difference methods for solving first and second order ordinary differential equations. International journal of applied mathematical research, 4, 316-324. 10.14419/ijamr.v4i2.4331
[12] Najafi, H. S. & Yaghoubi, A. R. (2014). Solving dynamic equation by the non-standard finite difference method. Journal of computer science & computational mathematics, 4 (4), 57-60.
[13] Yaghoubi, A. R. & Najafi, H. S. (2019). Non-standard finite difference schemes for investigating stability of a mathematical model of virus therapy for cancer. Applications and applied mathematics: an international journal, 14 (2), 805-819.
[14] Mickens, R. E. (2005). Advances in the applications of non-standard finite difference schemes. World Scientific, Singapore.
[15] Mickens, R. E. (2001). A non-standard finite difference scheme for a nonlinear PDE having diffusive shock wave solutions. Mathematics and computers in simulation,
55, 549-555.
https://doi.org/10.1016/S0378-4754(00)00309-8
[16] Mickens, R. E. (2003). A non-standard finite difference scheme for a fisher PDE having nonlinear diffusion. Comput. Math. Appl., 45, 429-436. https://doi.org/10.1016/S0898-1221(03)80028-7
[17] Mickens, R. E. (2005). A non-standard finite difference scheme for a PDE modeling combustion with nonlinear advection and diffusion. Mathematics and computers in simulation,
69, 439-446.
https://doi.org/10.1016/j.matcom.2005.03.008
[18] Mickens, R. E. (2007). Determination of denominator functions for a NSFD scheme for the fisher PDE with linear advection. Mathematics and computers in simulation,
74, 190-195.
https://doi.org/10.1016/j.matcom.2006.10.006
[19] Mickens, R. E. (2006). Calculation of denominator functions for non-standard finite difference schemes for differential equations satisfying a positivity condition. Wiley inter science,
23,
672-691.
https://doi.org/10.1002/nu.20198
)