Numerical Analysis of Tumor Model in Steady State

W. Allegretto, G. Cao, G. Li, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


In this paper we study the numerical approximation of the steady state tumor model proposed by Chaplain and Stuart [1] to describe the angiogenesis process through which new blood vessels are produced. The existence and convergence properties of finite difference approximation solutions are shown. More precisely, we also show that this numerical scheme preserves the structure properties earlier established for the analytical model. Furthermore we actually obtain improvements on the structure conditions given in [2]. Some numerical examples are also carried out to demonstrate our theoretical justifications.
Original languageEnglish
Pages (from-to)593-606
Number of pages14
JournalComputers and Mathematics with Applications
Issue number5
Publication statusPublished - 1 Sept 2006
Externally publishedYes


  • Finite difference
  • Maximum principle
  • Nonnegative solution
  • Steady state
  • Tumor modeling

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


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