Preliminary investigation on the numerical properties of a discretization of the hyperbolic Burgers-Fisher equation
DOI:
https://doi.org/10.33064/iycuaa2015653578Keywords:
hyperbolic Burgers-Fisher’s equation, traveling-wave solutions, nonlinear discretization, finite-difference method, positivity, boundedness, monotone techniqueAbstract
In this work, we provide a nonlinear, finite-difference scheme to approximate the solutions of a hyperbolic generalization of the Burgers-Fisher equation from population dynamics. The model under study is a partial differential equation with nonlinear
advection, reaction and damping terms, for which the existence of some traveling-wave solutions has been established in the literature. In the present manuscript, we investigate the capability of our technique to preserve some of the most important
features of those solutions, namely, the positivity, the boundedness and the monotonicity. The finitedifference approach followed in this work employs the exact solutions to prescribe the initial-boundary data. In addition to providing good approximations
to the analytical solutions, our simulations suggest that the method is also capable of preserving the mathematical features of interest.
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Copyright (c) 2015 Jorge Eduardo Macías Díaz, Jonathan Batres Romo
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