A PARADIGM FOR WELL-BALANCED SCHEMES FOR TRAVELING WAVES EMERGING IN PARABOLIC BIOLOGICAL MODELS - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

A PARADIGM FOR WELL-BALANCED SCHEMES FOR TRAVELING WAVES EMERGING IN PARABOLIC BIOLOGICAL MODELS

Résumé

We propose a methodology for designing well-balanced numerical schemes to investigate traveling waves in parabolic models from mathematical biology. We combine well-balanced techniques for parabolic models known in the literature with the so-called LeVeque-Yee formula as a dynamic estimate for the spreading speed. This latter formula is used to consider the evolution problem in a moving frame at each time step, where the equations admit stationary solutions, for which well-balanced techniques are suitable. Then, the solution is shifted back to the stationary frame in a well-balanced manner. We illustrate this methodology on parabolic reaction-diffusion equations, such as the Fisher/Kolmogorov-Petrovsky-Piskunov Equation, and a class of equations with a cubic reaction term that exhibit a transition from pulled to pushed waves. We show that the numerical schemes capture in a consistent way simultaneously the wave speed and, to an extent, the so-called Bramson delay.
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Dates et versions

hal-04055403 , version 1 (02-04-2023)

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Mete Demircigil, Benoit Fabreges. A PARADIGM FOR WELL-BALANCED SCHEMES FOR TRAVELING WAVES EMERGING IN PARABOLIC BIOLOGICAL MODELS. 2023. ⟨hal-04055403⟩
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