Analysis of the spectral meshless radial point interpolation for solving fractional reaction–subdiffusion equation

摘要

The present paper is devoted to the development of spectral meshless radial point interpolation (SMRPI) technique for solving fractional reaction–subdiffusion equation in one and two dimensional cases. The time fractional derivative is described in the Riemann–Liouville sense. The applied approach is based on a combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which act as basis functions in the frame of SMRPI. It is proved that the scheme is unconditionally stable with respect to the time variable in H1 and we show convergence order of the time discrete scheme is O(δtα), 0<α<1. In the current work, the thin plate splines (TPS) are used to construct the basis functions. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme.