an:05207595
Zbl 1121.92036
Allegretto, W.; Cao, G.; Li, G.; Lin, Y.
Numerical analysis of tumor model in steady state
EN
Comput. Math. Appl. 52, No. 5, 593-606 (2006).
00188761
2006
j
92C50 65M06
maximum principle; finite difference; tumor modeling; nonnegative solution
Summary: We study the numerical approximation of the steady state tumor model proposed by \textit{M. A. J. Chaplain} and \textit{A. M. Stuart} [IMA J. Math. Appl. Med. Biol. 10, No. 3, 149--168 (1993; Zbl 0783.92019)] 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 by \textit{W. Allegretto} et al. [J. Math. Biol. 35, No. 8, 949--966 (1997; Zbl 0892.92009)]. Some numerical examples are also carried out to demonstrate our theoretical justifications.
Zbl 0783.92019; Zbl 0892.92009