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A convergent numerical scheme for integrodifferential kinetic models of angiogenesis

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Bonilla, Luis L. and Carpio, Ana and Carretero, Manuel and Duro, Gema and Negreanu, Mihaela and Terragni, Filippo (2018) A convergent numerical scheme for integrodifferential kinetic models of angiogenesis. Journal of Computational Physics, 375 . pp. 1270-1294. ISSN 0021-9991

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Official URL: https://doi.org/10.1016/j.jcp.2018.09.008




Abstract

We study a robust finite difference scheme for integrodifferential kinetic systems of Fokker-Planck type modeling tumor driven blood vessel growth. The scheme is of order one and enjoys positivity features. We analyze stability and convergence properties, and show that soliton-like asymptotic solutions are correctly captured. We also find good agreement with the solution of the original stochastic model from which the deterministic kinetic equations are derived working with ensemble averages. A numerical study clarifies the influence of velocity cut-offs on the solutions for exponentially decaying data.


Item Type:Article
Uncontrolled Keywords:Kinetic model, Fokker–Planck, Integrodifferential, Angiogenesis
Subjects:Sciences > Mathematics > Differential equations
Sciences > Mathematics > Operations research
Medical sciences > Medicine > Cardiovascular system
ID Code:55851
Deposited On:18 Jun 2019 14:53
Last Modified:19 Jun 2019 07:51

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