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A convergent numerical scheme for integrodifferential kinetic models of angiogenesis. (English) Zbl 1416.92087

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.

MSC:

92C50 Medical applications (general)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R09 Integro-partial differential equations
45K05 Integro-partial differential equations
92-08 Computational methods for problems pertaining to biology

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