On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation - Publikacja - MOST Wiedzy

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On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation

Abstrakt

In this note, we establish analytically the convergence of a nonlinear finite-difference discretization of the generalized Burgers-Fisher equation. The existence and uniqueness of positive, bounded and monotone solutions for this scheme was recently established in [J. Diff. Eq. Appl. 19, 1907{1920 (2014)]. In the present work, we prove additionally that the method is convergent of order one in time, and of order two in space. Some numerical experiments are conducted in order to assess the validity of the analytical results.We conclude that the methodology under investigation is a fast, nonlinear, explicit, stable, convergent numerical technique that preserves the positivity, the boundedness and the monotonicity of approximations, making it an ideal tool in the study of some traveling-wave solutions of the mathematical model of interest. This note closes proposing new avenues of future research.

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Informacje szczegółowe

Kategoria:
Publikacja w czasopiśmie
Typ:
artykuł w czasopiśmie wyróżnionym w JCR
Opublikowano w:
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS nr 21, wydanie 4, strony 374 - 382,
ISSN: 1023-6198
Język:
angielski
Rok wydania:
2015
Opis bibliograficzny:
Szafrańska A., Macías-Díaz J.: On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation// JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS. -Vol. 21, iss. 4 (2015), s.374-382
DOI:
Cyfrowy identyfikator dokumentu elektronicznego (otwiera się w nowej karcie) 10.1080/10236198.2015.1016008
Weryfikacja:
Politechnika Gdańska

wyświetlono 19 razy

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