PARTICULAR SOLUTIONS FOR THE GENERALIZED BURGERS-HUXLEY EQUATION BY THE FACTORIZATION METHOD
Keywords:
Burgers-Huxley equation, factorization method, nonlinear differential equations, modeling, traveling waveAbstract
The article deals with numerical solutions of non-linear partial differential equations, such as the generalized Burgers-Huxley equations, which combine the effects of advection, diffusion, dispersion and non-linear transport. The Burgers-Huxley equation is solved numerically with the use of the factorization method, where a set of special solutions are obtained. It was shown that the factorization method is an efficient method with acceptable accuracy for solving the Burgers-Huxley equation
References
Y.N. Kyrychko, M.V. Bartuccelli and K.B. Blyuss, Persistence of travelling wave solutions of a fourth order diffusion system, Journal of Computation and Applied Mathematics, 176 (2005) 433-443.
A.G. Bratsos, A fourth-order numerical scheme for solving the modified Burgers equation, Computers and Mathematics with Applications, 60 (2010) 1393-1400.
A.L. Hodgkin and A.F. Huxley, A quantitative description of ion currents and its applications to conduction and excitation in nerve membranes, Journal of Physiology, 117 (1952) 500-544.
L.M. Berkovich, Factorization as a method of finding exact invariant solutions of the Kolmogorov-Petrovskii-Piskunov equation and the related Semenov and Zeldovich equations, Sov. Math. Dokl. 45 (1992) 162–167.
