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...
| Authors: | , , , , , |
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| Format: | article |
| Publication Date: | 2018 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/13407 |
| Online Access: | https://hdl.handle.net/20.500.14352/13407 |
| Access Level: | Open access |
| Keyword: | 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 |
| Summary: | 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. |
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