Positivity preserving high order schemes for angiogenesis models
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2022
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De Gruyter
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Carpio Rodríguez, A. M. y Cebrián, E. «Positivity Preserving High Order Schemes for Angiogenesis Models». International Journal of Nonlinear Sciences and Numerical Simulation, vol. 23, n.o 6, octubre de 2022, pp. 917-29. https://doi.org/10.1515/ijnsns-2021-0112.
Abstract
Hypoxy induced angiogenesis processes can be described by coupling an integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the angiogenic factor. We propose high order positivity preserving schemes to approximate the marginal tip density by combining an asymptotic reduction with weighted essentially non oscillatory and strong stability preserving time discretization. We capture soliton-like solutions representing blood vessel formation and spread towards hypoxic regions.