A convergent numerical scheme for integrodifferential kinetic models of angiogenesis Articles uri icon

publication date

  • December 2018

start page

  • 1270

end page

  • 1294

volume

  • 375

International Standard Serial Number (ISSN)

  • 0021-9991

Electronic International Standard Serial Number (EISSN)

  • 1090-2716

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. (C) 2018 Elsevier Inc. All rights reserved.

keywords

  • kinetic model; fokker-planck; integrodifferential; angiogenesis; fokker-planck equation; particle methods; streamline diffusion; tumor angiogenesis; vlasov; implicit; algorithm; space