Comparative Study of Radial Basis Functions for PDEs with Variable Coefficients

The radial basis functions(RBFs)play an important role in the numerical simulation processes of partial differential equations.Since the radial basis functions are meshless algorithms,its approximation is easy to implement and mathematically simple.In this paper,the commonly⁃used multiquadric RBF,conical RBF,and Gaussian RBF were applied to solve boundary value problems which are governed by partial differential equations with variable coefficients.Numerical results were provided to show the good performance of the three RBFs as numerical tools for a wide range of problems.It is shown that the conical RBF numerical results were more stable than the other two radial basis functions.From the comparison of three commonly⁃used RBFs,one may obtain the best numerical solutions for boundary value problems.