An element-free Galerkin method for the time-fractional subdiffusion equations

In this paper, an element-free Galerkin (EFG) method is developed for the numerical analysis of the time-fractional subdiffusion equation. By using the L2 - 1(sigma) formula to approximate the Caputo fractional derivative, a second-order accurate scheme is proposed to achieve temporal discretization. Then, time-independent integer-order boundary value problems are formed, and a stabilized EFG method is applied to establish the discretize linear algebraic systems. Error of the proposed meshless method is proved theoretically. Numerical results show the convergence and effectiveness of the method.