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A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains. (English) Zbl 1245.65144
Summary: 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.

MSC:
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35K57 Reaction-diffusion equations
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