An element-free Galerkin meshless method for simulating the behavior of cancer cell invasion of surrounding tissue

In the present work, we apply a meshless approach based on weak form namely element-free Galerkin for finding the numerical solution of the mathematical modelling of cancer cell invasion of tissue. A semi-implicit finite difference scheme based on backward Euler is also used for estimating the temporal variable. In order to verify this method, we have compared it numerically with another meshless technique i.e. generalized moving least squares approximation. The proposed method depends on a set of scattered points on the domain of the problem. Also, this approach is based on global weak form and requires a background cell for computing the numerical integrations. The studied model consists of a system of time-dependent reaction-diffusion-taxis partial differential equations describing the interactions between cancer cells, extracellular matrix and matrix degradation enzymes. At the end of this paper, we present some numerical simulations showing the behavior of cancer cell invasion of tissue at different times using regular and Halton points as well.