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- W2912752958 abstract "In this work, we investigate numerically some relevant solutions of a diffusion problem with a general reaction term. The system under investigation is governed by a partial differential equation that generalizes the classical Fisher's equation and the Hodgkin–Huxley model. In a first stage, we provide an equivalent presentation of the problem, and recall an explicit logarithmic numerical model to solve it. As one of the most important outcomes of this work, we prove that logarithmic scheme is a structure-preserving model under suitable conditions. Concretely, we show that the numerical model is capable of preserving the positivity, the boundedness and the monotonicity of the approximations. This feature of the numerical integrator is in agreement with the fact that the continuous model has solutions with the same characteristics. Also, for the first time in the literature, we show that the logarithmic models are consistent schemes which are stable and convergent. Some numerical simulations confirm that the numerical model is a convergent technique, with first order of convergence in time and second order in space." @default.
- W2912752958 created "2019-02-21" @default.
- W2912752958 creator A5055620640 @default.
- W2912752958 date "2019-06-01" @default.
- W2912752958 modified "2023-09-24" @default.
- W2912752958 title "On the numerical and structural properties of a logarithmic scheme for diffusion–reaction equations" @default.
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- W2912752958 doi "https://doi.org/10.1016/j.apnum.2019.01.015" @default.
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