automatic choice of shape parameter

RBF collocation path-following approach: optimal choice for shape parameter based on genetic algorithm

This paper presents a new method to solve a challenging problem and a topic of current research namely the selection of optimal shape parameters for the Radial Basis Function (RBF) collocation methods in  both interpolation and nonlinear Partial Differential Equations (PDEs) problems.  To this intent, a compromise must be made to achieve the conflict between accuracy and stability referred to as the trade-off  or uncertainty principle.  The use of genetic algorithm and path-following continuation allows us on the one hand to avoid the local optimum issue associated with RBF interpolation ma