Analysis of a meshless method for fractional diffusion-wave equation

In the current paper a numerical technique is proposed for solving the time fractional diffusionwave equation. Firstly, we change the main problem based on the Dirichlet boundary condition to a new problem based on the Robin boundary condition. Then, we obtain a semi-discrete scheme for the new problem with Robin boundary condition. We prove when $\beta\rightarrow +\infty$ solution of the semi-discrete scheme based on the Dirichlet boundary condition converges to the solution of the semi-discrete scheme based on the Robin boundary condition. We consider the new semi-discrete scheme with Robin boundary condition and use the meshless Galerkin method to approximate the spatial derivatives. Finally, we obtain an error bound for the new problem. We prove that convergence order of the numerical scheme based on Galekin meshless is O(h)