In this paper, we focus on fast solvers with linearithmic complexity in space for high-
dimensional time-fractional subdiffusion equations. Firstly, we present two alternating …

We develop a fast space-time finite difference method for space-time fractional diffusion
equations by fully utilizing the mathematical structure of the scheme. A circulant block …

In this paper, a high-order compact scheme is proposed for solving two-dimensional
nonlinear time-fractional fourth-order reaction-diffusion equations. The fractional derivative …

This paper is devoted to the construction and analysis of compact finite difference methods
for a class of time-fractional convection–reaction–diffusion equations with variable …

This paper is concerned with numerical methods for a class of time-fractional convection-
reaction-diffusion equations. The convection and reaction coefficients of the equation may …

In this paper, we propose two new approximation methods on a general mesh for the
generalized Caputo fractional derivative of order α∈(0, 1). The accuracy of these two …

It is well known that using high-order numerical algorithms to solve fractional differential
equations leads to almost the same computational cost with low-order ones but the accuracy …

In this paper, we study preconditioners for all-at-once systems arising from the discretization
of time-fractional sub-diffusion equations. Due to the use of high-order accurate formulas in …

In this paper, based on the nonuniform time meshes, we proposed an efficient difference
scheme for solving the time-fractional bi-flux diffusion equation. By the energy method, we …

In this paper we derive the fourth-order asymptotic expansions of the trapezoidal
approximation for the fractional integral and the $ L1 $ approximation for the Caputo …