Second order characteristic based schemes for chemotaxis system
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Second order characteristic based schemes for the first equation of the cheomtaxis system are presented. The derived schemes belong to the finite volume methods in which the data points are the cell centres. The solutions are approximated by piecewise linear functions in 1D while piecewise bilinear functions are used in 2D case. The schemes are shown to be mass conservative. The consistency and stability are discussed analytically. Numerical experiments are provided to back up the analysis. Some directions for future work is posted.