Numerical analysis: 4th ed
Discretizations of nonlinear differential equations using explicit nonstandard methods
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Finite-difference schemes for nonlinear wave equation that inherit energy conservation property
Journal of Computational and Applied Mathematics
A nonstandard finite-difference scheme for the Lotka--Volterra system
Applied Numerical Mathematics
Symmetry-preserving discretization of turbulent flow
Journal of Computational Physics
Exact multiplicity of boundary blow-up solutions for a bistable problem
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Mathematical modeling of bioremediation of trichloroethylene in aquifers
Computers & Mathematics with Applications
Non-standard numerical method for a mathematical model of RSV epidemiological transmission
Computers & Mathematics with Applications
An efficient implementation of a numerical method for a chemotaxis system
International Journal of Computer Mathematics - RECENT ADVANCES IN COMPUTATIONAL AND APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING
Uniformly constructing soliton solutions and periodic solutions to Burgers-Fisher equation
Computers & Mathematics with Applications
Persistence of travelling wave solutions of a fourth order diffusion system
Journal of Computational and Applied Mathematics
A nonstandard numerical scheme of predictor-corrector type for epidemic models
Computers & Mathematics with Applications
An analytical study for Fisher type equations by using homotopy perturbation method
Computers & Mathematics with Applications
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In this article, we propose a non-standard, finite-difference scheme to approximate the solutions of a generalized Burgers-Huxley equation from fluid dynamics. Our numerical method preserves the skew-symmetry of the partial differential equation under study and, under some analytical constraints of the model constants and the computational parameters involved, it is capable of preserving the boundedness and the positivity of the solutions. In the linear regime, the scheme is consistent to first order in time (due partially to the inclusion of a tuning parameter in the approximation of a temporal derivative), and to second order in space. We compare the results of our computational technique against the exact solutions of some particular initial-boundary-value problems. Our simulations indicate that the method presented in this work approximates well the theoretical solutions and, moreover, that the method preserves the boundedness of solutions within the analytical constraints derived here. In the problem of approximating solitary-wave solutions of the model under consideration, we present numerical evidence on the existence of an optimum value of the tuning parameter of our technique, for which a minimum relative error is achieved. Finally, we linearly perturb a steady-state solution of the partial differential equation under investigation, and show that our simulations still converge to the same constant solution, establishing thus robustness of our method in this sense.