A bounded and monotone finite-difference solution of a hyperbolic Burgers–Fisher equation

L. A. Flores-Oropeza (), A. Román-Loera and Ahmed S. Hendy
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L. A. Flores-Oropeza: Departamento de Sistemas Electrónicos, Universidad Autónoma de Aguascalientes, Avenida, Universidad 940, Ciudad Universitaria, Aguascalientes, Ags. 20131, Mexico
A. Román-Loera: Departamento de Sistemas Electrónicos, Universidad Autónoma de Aguascalientes, Avenida, Universidad 940, Ciudad Universitaria, Aguascalientes, Ags. 20131, Mexico
Ahmed S. Hendy: #x2020;Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, ul. Mira. 19, Yekaterinburg 620002, Russia‡Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt

International Journal of Modern Physics C (IJMPC), 2018, vol. 29, issue 12, 1-12

Abstract: In this work, a nonlinear finite-difference scheme is provided 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. The existence of some traveling-wave solutions for this model 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 finite-difference 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.

Keywords: Hyperbolic Burgers–Fisher equation; traveling-wave solutions; nonlinear discretization; finite-difference method; positivity and boundedness; monotonicity (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S012918311850122X

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