We propose two preconditioners based on the fast sine transformation for solving linear
systems with ill-conditioned multilevel Toeplitz structure. These matrices are generated by …

The current study investigates the asymptotic spectral properties of a finite difference
approximation of nonlocal Helmholtz equations with a Caputo fractional Laplacian and a …

In this paper, we present a nonlocal perfectly matched layer (PML) for the nonlocal wave
equation in two dimensions, and design numerical discretization to solve the reduced PML …

In this paper, we propose an efficient preconditioner for the linear systems arising from the
one-sided space fractional diffusion equation with variable coefficients. The shifted Gr ̈ uu¨ …

In this paper, we solve the Helmholtz equation with multigrid preconditioned Krylov
subspace methods. The class of shifted Laplacian preconditioners is known to significantly …

In this paper, we firstly explore the special structure of the discretized linear systems from the
spatial fractional diffusion equations. The coefficient matrices of the resulting discretized …

Spectral and spectral element methods using Galerkin type formulations are efficient for
solving linear fractional PDEs (FPDEs) of constant order but are not efficient in solving …

In this paper, we consider numerical methods for Toeplitz-like linear systems arising from the
one-and two-dimensional Riesz space fractional diffusion equations. We apply the Crank …

In this paper, we analyze the spectra of the preconditioned matrices arising from discretized
multi-dimensional Riesz spatial fractional diffusion equations. The finite difference method is …

The fractional diffusion equation is discretized by an implicit finite difference scheme with the
shifted Grünwald formula, which is unconditionally stable. The coefficient matrix of the …