Abstract
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.
Highlights
Let R+ represent the set of positive numbers, let R+ = R+ ∪ { } and suppose that α and γ are real numbers such that < γ
5 Conclusions and perspectives In this note, we extended dimensionally a numerical technique to approximate the solution of the well-known Burgers-Huxley equation, using a finite-difference perspective
We established that the method is convergent of first order in time and second order in space
Summary
Problem Are there analytical results that guarantee the existence and uniqueness of positive and bounded solutions of the Burgers-Huxley equation? The following results are the most important properties on the existence and uniqueness of positive and bounded solutions of the Burgers-Huxley equation.
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