Fast second-order implicit difference schemes for time distributed-order and Riesz space fractional diffusion-wave equations

In this paper, fast numerical methods are established to solve a class of time distributed-order and Riesz space fractional diffusion-wave equations. We derive new difference schemes by weighted shifted Grünwald formula in centered space. The unconditional stability second-order convergence time, the analyzed. one-dimensional case, Gohberg-Semencul utilizing preconditioned Krylov subspace method is developed Toeplitz linear system derived from proposed scheme. two-dimensional we also design global conjugate gradient with truncated preconditioner resulting Sylvester matrix prove that spectrums matrices both cases clustered around 1, such preconditioners converge very quickly. Some experiments carried out demonstrate effectiveness show performances solution algorithms better than other testing methods.