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.
Citation: Z. Jackiewicz, B. Zubik-Kowal, B. Basse. Finite-difference and pseudo-spectral methodsfor the numerical simulations of in vitro human tumor cellpopulation kinetics[J]. Mathematical Biosciences and Engineering, 2009, 6(3): 561-572. doi: 10.3934/mbe.2009.6.561
Abstract
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.