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A Structure-Preserving Modified Exponential Method for the Fisher–Kolmogorov Equation |
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PP: 69-77 |
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doi:10.18576/amis/110109
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Author(s) |
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Jorge E. Macıas-Dıaz,
Stefania Tomasiello,
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Abstract |
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| In this work, we propose an exponential-type discretization of the well-known Fisher’s equation from population dynamics.
Only non-negative, bounded and monotone solutions are physically relevant in this note, and the discretization that we provide is able to
preserve these properties. The method is a modified explicit exponential technique which has the advantage of requiring a small amount
of computational resources and computer time. It is worthwhile to notice that our technique has the advantage over other exponentiallike
methodologies that it yields no singularities. In addition, the preservation of the properties of non-negativity, boundedness and
monotonicity are distinctive features of our method. As consequences of the analytical properties of the technique, the method is
capable of preserving the spatial and the temporal monotonicity of solutions. Qualitative and quantitative numerical simulations assess
the convergence properties of the finite-difference scheme proposed in this manuscript. |
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