An improved spectral meshless radial point interpolation for a class of time-dependent fractional integral equations: 2D fractional evolution equation

In this paper, a kind of spectral meshless radial point interpolation (SMRPI) technique is applied to the fractional evolution equation in two-dimensional for arbitrary fractional order. The applied approach is based on erudite 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 play as basis functions in the frame of SMRPI. In the current work, the thin plate splines (TPS) are used as the basis functions, and also the discretization technique employed is patterned after an idea of Ch. Lubich. It is proved the scheme is unconditional stable with respect to the time variable in L2-norm and convergent by the order of convergence O(δt1+α), 0<α<1. The results of numerical experiments are compared with analytical solution to confirm the accuracy and efficiency of the presented scheme. Three numerical examples, show that the SMRPI has reliable accuracy in irregular domains.