Positivity preserving high order schemes for angiogenesis models

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...

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Detalles Bibliográficos
Autores: Carpio, Ana, Cebrián de Barrio, Elena
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Universidad de Burgos (UBU)
Repositorio:Repositorio Institucional de la Universidad de Burgos (RIUBU)
OAI Identifier:oai:riubu.ubu.es:10259/8314
Acceso en línea:http://hdl.handle.net/10259/8314
Access Level:acceso abierto
Palabra clave:Angiogenesis
Asymptotic reduction
Fokker–Planck
High order schemes
Kinetic models
Positivity preserving
Matemáticas
Mathematics
Descripción
Sumario: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.