Simulation of activator–inhibitor dynamics based on cross-diffusion Brusselator reaction–diffusion system via a differential quadrature-radial point interpolation method (DQ-RPIM) technique

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The current paper proposes an efficient numerical procedure for solving the two-dimensional Brusselator reaction–diffusion system. First, the time derivative is discretized by a semi-implicit finite difference scheme such that the nonlinear terms are approximated by using one term of the Taylor expansion. It is shown if the nonlinear terms satisfy the Lipshitz condition, then the proposed difference scheme is stable. In the next, the spatial derivative is discretized by the differential quadrature technique based upon the shape functions of radial point interpolation method. We study some practical problems to show the efficiency and acceptable results of the developed technique.