A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains

Abstract Time-dependent advection–diffusion–reaction and diffusion–reaction equations are used as models in biology, chemistry, physics, and engineering. As representative examples, we focus on a chemotaxis model and a Turing system from biology and apply a local radial basis function method to numerically approximate the solutions. The numerical method can efficiently approximate large scale problems in complexly shaped domains.

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