A fast finite difference/RBF meshless approach for time fractional convection-diffusion equation with non-smooth solution

Abstract

In this paper, we propose a fast finite difference/RBF meshless method for time fractional convection-diffusion equation with singularity at the initial moment. Firstly, the time fractional derivative term is discretized by classical L1 format on graded meshes, and the spatial derivative term is approximated by meshless method. The meshless method does not need to construct meshes, which is more conducive for dealing with complex regions or complex boundary conditions. In addition, we adopt proper orthogonal decomposition (POD) technology to derive reduced-order RBF meshless extrapolation algorithm, which effectively reduces the amount of calculation and improves the calculation efficiency. Finally, the accuracy and efficiency of the method are verified by numerical examples.