An improved meshless algorithm for a kind of fractional cable problem with error estimate

Abstract

The present paper is devoted to the development of a kind of spectral meshless radial point interpolation (SMRPI) technique for solving fractional cable 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 the scheme is unconditional stable with respect to the time variable in H1 and convergent by the order of convergence O(δtγ), 0 < γ < 1. In the current work, the thin plate splines (TPS) are used as the basis functions. The results of numerical experiments are compared with analytical solution to confirm the accuracy and efficiency of the presented scheme.