Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization a` la Mickens of the generalized Burgers–Huxley equation.

J. E. Macías-Díaz; Anna Szafrańska

Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization a` la Mickens of the generalized Burgers–Huxley equation.

Abstract

Departing from a generalized Burgers–Huxley partial differential equation, we provide a Mickens-type, nonlinear, finite-difference discretization of this model. The continuous system is a nonlinear regime for which the existence of travelling-wave solutions has been established previously in the literature. We prove that the method proposed also preserves many of the relevant characteristics of these solutions, such as the positivity, the boundedness and the spatial and the temporal monotonicity. The main results provide conditions that guarantee the existence and the uniqueness of monotone and bounded solutions of our scheme. The technique was implemented and tested computationally, and the results confirm both a good agreement with respect to the travelling-wave solutions reported in the literature and the preservation of the mathematical features of interest.

Authors (2)

J. E. Macías-Díaz
- Universidad Autonoma de Aguascalientes, ..
Anna Szafrańska dr inż.

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Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS no. 20, edition 7, pages 989 - 1004,
ISSN: 1023-6198
Language:: English
Publication year:: 2014
Bibliographic description:: Macías-Díaz J., Szafrańska A.: Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization a` la Mickens of the generalized Burgers–Huxley equation.// JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS. -Vol. 20, iss. 7 (2014), s.989-1004
Verified by:: Gdańsk University of Technology