A Structure-Preserving Modified Exponential Method for the Fisher–Kolmogorov Equation

Authors

Jorge E. Macıas-Dıaz, Departamento de Matem´aticas y F´ısica, Universidad Aut´onoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes, Ags. 20131, MexicoFollow
Stefania Tomasiello, Consorzio di Ricerca Sistemi ad Agenti, Dipartimento di Ingegneria dell’Informazione e Elettrica, Matematica Applicata, Universit`a degli Studi di Salerno, Via Giovanni Paolo II 132, 84084 Fisciano, Salerno, ItalyFollow

Author Country (or Countries)

Mexico

Abstract

In this work, we propose an exponential-type discretization of the well-known Fisher’s equation from population dynamics. Only non-negative, bounded and monotone solutions are physically relevant in this note, and the discretization that we provide is able to preserve these properties. The method is a modified explicit exponential technique which has the advantage of requiring a small amount of computational resources and computer time. It is worthwhile to notice that our technique has the advantage over other exponentiallike methodologies that it yields no singularities. In addition, the preservation of the properties of non-negativity, boundedness and monotonicity are distinctive features of our method. As consequences of the analytical properties of the technique, the method is capable of preserving the spatial and the temporal monotonicity of solutions. Qualitative and quantitative numerical simulations assess the convergence properties of the finite-difference scheme proposed in this manuscript.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/110109

Recommended Citation

E. Macıas-Dıaz, Jorge and Tomasiello, Stefania (2017) "A Structure-Preserving Modified Exponential Method for the Fisher–Kolmogorov Equation," Applied Mathematics & Information Sciences: Vol. 11: Iss. 1, Article 9.
DOI: http://dx.doi.org/10.18576/amis/110109
Available at: https://digitalcommons.aaru.edu.jo/amis/vol11/iss1/9