On the new variable shape parameter strategies for radial basis functions

One of the most popular meshless methods is constructed by radial kernels as basis called radial basis function method. It has a unique feature which affects significantly on accuracy and stability of approximation: existence of a free parameter known as shape parameter that can be chosen constantly or variably. Several techniques for selecting a variable shape parameter have been presented in the older works. Our study focuses on investigating the deficiency of these techniques and we introduce two new alternative strategies called hybrid shape parameter and binary shape parameter strategies based on the advantages of older studies. The proposed approaches produce the more accurate results as shown in numerical results where they are compared with random shape parameter strategy for interpolating one-dimensional and two- dimensional functions as well as in approximating the solution of Poisson equation.