A convergent numerical scheme for integrodifferential kinetic models of angiogenesis

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 soluti...

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Detalles Bibliográficos
Autores: Bonilla, Luis L., Carpio Rodríguez, Ana María, Carretero Zamora, Juan Manuel, Duro, Gema, Negreanu Pruna, Mihaela, Terragni, Filippo
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/13407
Acceso en línea:https://hdl.handle.net/20.500.14352/13407
Access Level:acceso abierto
Palabra clave:519.8
517.9
Kinetic model
Fokker–Planck
Integrodifferential
Angiogenesis
Ecuaciones diferenciales
Investigación operativa (Matemáticas)
Sistema cardiovascular
1202.07 Ecuaciones en Diferencias
1207 Investigación Operativa
2411.03 Fisiología Cardiovascular
Descripción
Sumario: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.