On the Numerical Solutions of One and Two-Stage Model of Carcinogenesis Mutations with Time Delay and Diffusion
- 1 Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan
Abstract
In this paper , we focused on numerical solutions of carcinogenesis mutations models that are based on reaction-dif fusion systems and Lotka-Volterra food chains. We consider the case with one and two-stages of mutations with appro priate initial conditions and the zero-flux boundary conditions. The main purpose is to construct a stable discretization scheme, which allows much accuracy than those of a standard approach. To this end, we use the spectral method to postprocess numerical solutions for the proposed model by using some classical methods for solving differential equa tions. The implementation of the algorithm is simple and it does not need to solve the linear or nonlinear system (in case the model is nonlinear). We simulate the one and two-stage carcinogenesis mutations model and compared the results with previously published ones.
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