Pattern Formation Simulations In Reaction-diffusion Systems By Local Integral Equation Method
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V. Sladek, J. Sladek & A. Shirzadi
A meshless Local Integral Equation (LIE) method is proposed for numerical simulation of 2D pattern formation in nonlinear reaction-diffusion systems. The method works with weak formulation of the differential governing equations on local sub-domains with using the Green function of the Laplace operator as the test function. The Moving Least Square (MLS) approximation is employed for spatial variations of field variables while the time evolution is discretized by using suitable finite difference approximations. The effects of model parameters and conditions are studied by considering the well known Schnakenberg model. Keywords: nonlinear reaction-diffusion systems, Turing instability, pattern formation, Schnakenberg model, meshless methods, local integral equations, moving least squares, finite differences.
nonlinear reaction-diffusion systems, Turing instability, pattern formation, Schnakenberg model, meshless methods, local integral equations, moving least squares, finite differences