COMPUTING HIGHLY ACCURATE SOLUTIONS OF A TUMOUR ANGIOGENESIS MODEL
作者： J. VALENCIANO , M. A. J. CHAPLAIN
DOI: 10.1142/S0218202503002702
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摘要: In this paper we describe and implement a numerical method which provides highly accurate solutions of a generic two-dimensional model for the formation of capillary networks as a partial process in tumour angiogenesis. The model includes effects due to diffusion, chemotaxis, haptotaxis and cell proliferation. The governing partial differential equation is a diffusion-advection-reaction equation of parabolic type. In order to achieve high accuracy in space, we use a semi-discretisation based on the spectral element method …
sci-hub.se 参考文章(25)
F.A. Davidson, A.R.A. Anderson, M.A.J. Chaplain, Steady-state solutions of a generic model for the formation of capillary networks Applied Mathematics Letters. ,vol. 13, pp. 127- 132 ,(2000) , 10.1016/S0893-9659(00)00044-6
M.A.J. Chaplain, M. Ganesh, I.G. Graham, Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth Journal of Mathematical Biology. ,vol. 42, pp. 387- 423 ,(2001) , 10.1007/S002850000067
Gilbert Strang, George J. Fix, D. S. Griffin, An Analysis of the Finite Element Method ,(1973)
Alexander RA Anderson, Mark AJ Chaplain, Continuous and Discrete Mathematical Models of Tumor-induced Angiogenesis Bulletin of Mathematical Biology. ,vol. 60, pp. 857- 899 ,(1998) , 10.1006/BULM.1998.0042
AVNER FRIEDMAN, FERNANDO REITICH, ON THE EXISTENCE OF SPATIALLY PATTERNED DORMANT MALIGNANCIES IN A MODEL FOR THE GROWTH OF NON-NECROTIC VASCULAR TUMORS Mathematical Models and Methods in Applied Sciences. ,vol. 11, pp. 601- 625 ,(2001) , 10.1142/S021820250100101X
Razvan A. Satnoianu, John H. Merkin, Stephen K. Scott, Forced convective structures in a differential-flow reactor Dynamics and Stability of Systems. ,vol. 14, pp. 275- 298 ,(1999) , 10.1080/026811199282001
Philip J. Davis, Methods of Numerical Integration ,(1967)
Karol Z. Korczak, Anthony T. Patera, An isoparametric spectral element method for solution of the Navier-Stokes equations in complex geometry Journal of Computational Physics. ,vol. 62, pp. 361- 382 ,(1986) , 10.1016/0021-9991(86)90134-8
B.D. Sleeman, A.R.A. Anderson, M.A.J. Chaplain, A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation Applied Mathematics Letters. ,vol. 12, pp. 121- 127 ,(1999) , 10.1016/S0893-9659(99)00132-9
MR Myerscough, PK Maini, KJ Painter, Pattern Formation in a Generalized Chemotactic Model Bulletin of Mathematical Biology. ,vol. 60, pp. 1- 26 ,(1998) , 10.1006/BULM.1997.0010