Positivity preserving high order schemes for angiogenesis models-Reference-Cited by-同舟云学术

Positivity preserving high order schemes for angiogenesis models

Published:2021-04-09 Issue:0 Volume:0 Page:
ISSN:1565-1339
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Carpio A.¹,Cebrian E.²

Affiliation:

1. Departamento de Matematica Aplicada , Universidad Complutense , 28040 Madrid , Spain

2. Departamento de Matematicas y Computación , Universidad de Burgos , 09001 Burgos , Spain

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2021-0112/pdf

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