Some remarks on an exact and dynamically consistent scheme for the Burgers-Huxley equation in higher dimensions

Departing from a finite-difference scheme to approximate the solutions of the Burgers-Huxley equation, the present manuscript extends that technique to higher dimensions. We show that our methodology possesses the same numerical properties of the one-dimensional version (exactness, positivity, bound...

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Bibliographic Details
Published in:Advances in difference equations 2015-12, Vol.2015 (1), p.1-10, Article 386
Main Authors: Macias-Diaz, Jorge Eduardo, Gonzalez, Ana E
Format: Article
Language:English
Subjects:
Analysis
Approximation
Difference and Functional Equations
Difference equations
Existence theorems
Finite difference method
Functional Analysis
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Uniqueness
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Summary:Departing from a finite-difference scheme to approximate the solutions of the Burgers-Huxley equation, the present manuscript extends that technique to higher dimensions. We show that our methodology possesses the same numerical properties of the one-dimensional version (exactness, positivity, boundedness, monotonicity, etc. ). Moreover, helped by a recent theorem on the existence and uniqueness of positive and bounded solutions of the Burgers-Huxley equation, we establish that the present method is a convergent scheme.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-015-0730-1