Abstract
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 language | English |
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Pages (from-to) | 593-606 |
Number of pages | 14 |
Journal | Computers and Mathematics with Applications |
Volume | 52 |
Issue number | 5 |
DOIs | |
Publication status | Published - 1 Sept 2006 |
Externally published | Yes |
Keywords
- Finite difference
- Maximum principle
- Nonnegative solution
- Steady state
- Tumor modeling
ASJC Scopus subject areas
- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics