American Institute of Mathematical Sciences

Advanced
2009, 6(3): 561-572. doi: 10.3934/mbe.2009.6.561

Finite-difference and pseudo-spectral methods for the numerical simulations of in vitro human tumor cell population kinetics

Z. Jackiewicz 1, , B. Zubik-Kowal 2, and  B. Basse 3,

1. 

Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287, United States
2. 

Department of Mathematics, Boise State University, 1910 University Drive, Boise, Idaho 83725, United States
3. 

Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, New Zealand

Received  January 2008 Revised  February 2009 Published  June 2009

Pseudo-spectral approximations are constructed for the model equations describing the population kinetics of human tumor cells in vitro and their responses to radiotherapy or chemotherapy. These approximations are more efficient than finite-difference approximations. The spectral accuracy of the pseudo-spectral method allows us to resolve the model with a much smaller number of spatial grid-points than required for the finite-difference method to achieve comparable accuracy. This is demonstrated by numerical experiments which show a good agreement between predicted and experimental data.
Keywords: mathematical model, cell cycle dynamics, pseudo-spectral methods, Population kinetics of human cancer cells in vitro, human tumor cells, finite-difference methods..
Mathematics Subject Classification: Primary: 45K05, 34K28; Secondary: 62P1.
Citation: Z. Jackiewicz, B. Zubik-Kowal, B. Basse. Finite-difference and pseudo-spectral methods for the numerical simulations of in vitro human tumor cell population kinetics. Mathematical Biosciences & Engineering, 2009, 6 (3) : 561-572. doi: 10.3934/mbe.2009.6.561
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