Investigation of the use of radial basis functions in local collocation method for solving diffusion problems

Abstract

Multidimensional diffusion problems can be solved by a local collocation method using radial basis functions. This method is computationally efficient because it is meshless and yields a sparse system of algebraic equations. Three types of radial basis functions—the generalized multiquadric function, the Gaussian function, and the generalized thin-plate spline function—are considered as interpolation functions in this method. Analysis of truncation error indicates that the use of the generalized multiquadric function or the Gaussian function produces satisfactory results, but the generalized thin-plate spline function is not a good interpolation function.