| dc.description.abstract | In this paper, we consider a model for the population kinetics of human tumor cells in vitro, differentiated
by phases of the cell division cycle and length of time within each phase. Since it is not easy to isolate the
effects of cancer treatment on the cell cycle of human cancer lines, during the process of radiotherapy or chemotherapy,
therefore, we include the spatial effects of cells in each phase and analyse the extended model. The extended
model is not easy to solve analytically, because perturbation by cancer therapy causes the flow cytometric profile
to change in relation to one another. Hence, making it difficult for the resulting model to be solved analytically.
Thus, in [16] it is reported that the non-standard schemes are reliable and propagate sharp fronts accurately, even
when the advection, reaction processes are highly dominant and the initial data are not smooth. As a result, we
construct a fitted operator finite difference method (FOFDM) coupled with non-standard finite difference method
(NSFDM) to solve the extended model. The FOFDM and NSFDM are analyzed for convergence and are seen that
they are unconditionally stable and have the accuracy of O(Dt +(Dx)2), where Dt and Dx denote time and space
step-sizes, respectively. Some numerical results confirming theoretical observations are presented. | en_US |
