Pseudo-spectral approximations are constructed for the model equations which describe 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.
This is an author-produced, peer-reviewed version of this article. The final, definitive version of this document can be found online at Mathematical Biosciences and Engineering, published by American Institute of Mathematical Sciences. Copyright restrictions may apply. DOI: 10.3934/mbe.2009.6.561
Jackiewicz, Z.; Zubik-Kowal, Barbara; and Basse, B.. (2009). "Finite-Difference and Pseudo-Sprectral Methods for the Numerical Simulations of In Vitro Human Tumor Cell Population Kinetics". Mathematical Biosciences and Engineering, 6(3), 561-572. http://dx.doi.org/10.3934/mbe.2009.6.561