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On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation
Abstract
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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Authors (2)
-
J.e. Macías-Díaz
- Universidad Autonoma de Aguascalientes Departamento de Matemáticas y Física
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Details
- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
no. 21,
edition 4,
pages 374 - 382,
ISSN: 1023-6198 - Language:
- English
- Publication year:
- 2015
- Bibliographic description:
- 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:
- Digital Object Identifier (open in new tab) 10.1080/10236198.2015.1016008
- Verified by:
- Gdańsk University of Technology
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