When one solves differential equations, modeling biological or physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. In this work, we introduce explicit finite difference schemes based on the nonstandard discretization method to approximate solution of the cross-diffusion system from bioscience. The proposed schemes improve the accuracy and guarantee the positivity requirement, as is demanded for the solution of such system. We apply new methods for numerical integration of the cancer growth model for illustrating the performance of them.
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