On the computational modeling of traveling-wave solutions of a nonlinear population equation
DOI:
https://doi.org/10.33064/iycuaa2013574014Keywords:
parabolic partial differential equation, reaction-difusion model, square-root law, finite-difference method, positivity and boundedness, monotonicityAbstract
Departing from a diffusive partial differential equation with nonlinear reaction, we developed a non-standard, finite-difference scheme to approximate its solutions. The reaction term of the mathematical model follows a square-root regime, and the existence of traveling-wave solutions for this equation is a fact recently established in the specialized literature. In the present manuscript,
we propose a discretization which preserves most of the mathematical features of such solutions, namely, the positivity, the elevation mark, and the temporal and the spatial monotony. We provide here some illustrative simulations that evidence the preservation of such properties.
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Copyright (c) 2013 Jorge Eduardo Macías Díaz
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