A numerical method for solving the one-dimensional heat and advection-diffusion equation using radial basis functions

In this paper, we introduce radial basis functions and the use of these basis functions is discussed for solving parabolic equations. We propose a numerical scheme and approximate the solution using Laguerre-Gaussians radial basis functions (LG-RBFs). This method will be used to reduce the problem to a set of algebraic equations. The results of numerical experiments are presented and compared with the other radial basis functions and the results of other methods to confirm the validity of this method.