Numerical and analytical investigations for solving the inverse tempered fractional diffusion equation via interpolating element-free Galerkin (IEFG) method

This manuscript is devoted to analysis of a novel meshless numerical procedure for solving the inverse tempered fractional diffusion equation. The employed numerical technique is based on a modification of element-free Galerkin (EFG) method, and the shape functions of interpolating moving least squares approximation are utilized for ingredients of the test and trial functions. At the first stage, the time derivative is discretized by a Crank-Nicolson idea to derive a semi-discrete scheme. In the next stage, the space variable is approximated by the EFG procedure. The convergence rate and stability of the time-discrete formulation are analyzed. Furthermore, the error estimate of the full-discrete plan is discussed in detail. In the end, some numerical experiments are investigated to check the theoretical results and the efficiency of the developed technique.