| Radial basis function (RBF) methods are a relatively new (1990s) method to numerically approximate the solution of partial differential equations (PDEs). RBF methods can be implemented both globally and locally. Comparisons between these two techniques will be made in this work to illustrate how the local method can obtain similar accuracy to the global method while only using a small subset of available points, and thus using substantially less computer memory. Finally, RBF methods will be applied to solve systems of nonlinear PDEs that model pattern formation in mathematical biology. The local RBF method will be used to evaluate Turing pattern and chemotaxis models that are both modeled by advection-reaction-diffusion type PDEs. |
