A Meshless Local Radial Point Collocation Method for Simulating the Time-Fractional Convection-Diffusion Equations on Surfaces

Abstract

The time-fractional problem is a class of important models to represent the real world. It is an open problem to study how the fractional operator acts on the surface. In this work, we present and analyze a meshless local radial point collocation method for numerically solving time-fractional convection-diffusion equations on closed surfaces embedded in [Formula: see text]. The second-order shifted Grünwald scheme is applied in time discretization. All computations use only extrinsic coordinates to avoid coordinate distortions and singularities. Moreover, the stability and convergence of the method are proven by the energy estimate. Numerical experiments are provided to support the convergence analysis and numerical performance of the proposed method.