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

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

Abstrakt

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.

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Kategoria:
Publikacja w czasopiśmie
Typ:
artykuł w czasopiśmie wyróżnionym w JCR
Opublikowano w:
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS nr 20, wydanie 7, strony 989 - 1004,
ISSN: 1023-6198
Język:
angielski
Rok wydania:
2014
Opis bibliograficzny:
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
Weryfikacja:
Politechnika Gdańska

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