An Element-Free Galerkin Method for Time-Fractional Diffusion-Wave Equations

Abstract

Numerical solution and theoretical error analysis of the element-free Galerkin (EFG) method were presented for the time-fractional diffusion-wave equations in the sense of Caputo. Through discretization of the time variables in the equation with the L1 approximate formula, the time-fractional diffusion-wave equation was transformed into a series of time-independent integer-order differential equations. Then, the penalty method was used to deal with the Dirichlet boundary condition and the EFG method was used to discretize the integer-order differential equations. Error estimates of the EFG method for the time-fractional diffusion-wave equations were derived theoretically. Finally, several numerical examples show the accuracy and effectiveness of the proposed meshless method.