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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 11 > No. 1


A Structure-Preserving Modified Exponential Method for the Fisher–Kolmogorov Equation

PP: 69-77
Jorge E. Macıas-Dıaz, Stefania Tomasiello,
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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