The local integral equation method for pattern formation simulations in reaction–diffusion systems

A meshless local integral equation (LIE) method is proposed for numerical simulation of 2D pattern formation in nonlinear reaction diffusion systems. The method uses 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 effect of parameters and conditions are studied by considering the well known Schnakenberg model.