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On the convergence of a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation
Abstract
In this note, we establish the property of convergence for a finite-difference discretization of a diffusive partial differential equation with generalized Burgers convective law and generalized Hodgkin–Huxley reaction. The numerical method was previously investigated in the literature and, amongst other features of interest, it is a fast and nonlinear technique that is capable of preserving positivity, boundedness and monotonicity. In the present work, we establish that the method is convergent with linear order of convergence in time and quadratic order in space. Some numerical experiments are provided in order to support the analytical results.
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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. 20,
pages 1444 - 1451,
ISSN: 1023-6198 - Language:
- English
- Publication year:
- 2014
- Bibliographic description:
- Szafrańska A., Macías-Díaz J.: On the convergence of a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation// JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS. -Vol. 20, nr. 10 (2014), s.1444-1451
- DOI:
- Digital Object Identifier (open in new tab) 10.1080/10236198.2014.936319
- Verified by:
- Gdańsk University of Technology
Referenced datasets
- dataset Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0,1].
- dataset Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0, γ^(1/p)].
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