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 …

In this work, we present a high-order numerical method for the two-dimensional nonlinear
space-fractional complex Ginzburg-Landau equation (FCGLE). Firstly, a fourth-order …

Combining the scale auxiliary variable (SAV) approach with leapfrog finite difference
methods, an unconditional energy-stable, non-couple and linearly implicit numerical …

In this paper, a numerical method to solve the multi-dimensional spatial fractional Allen–
Cahn equations has been investigated. After semi-discretizating the equations, a system of …

In this paper, we propose four time marching schemes for the two-mode phase field crystal
equation with the periodic boundary condition. The first-and second-order schemes are …

For the two-mode phase field crystal models, the evolutions of the solutions and energy vary
fast at certain time. To resolve varying time scales efficiently and reduce the computational …

In this paper, we propose first-and second-order exponential scalar auxiliary variable
(ESAV) schemes for solving the phase field crystal equation with the periodic boundary …

In this paper, we study a new splitting method for the semi-linear system of ordinary
differential equation, where the linear part is stiff. Firstly, the stiff part is split into two parts …

In this paper, we study the numerical solutions of the multi-dimensional spatial fractional
Allen-Cahn equations. After semi-discretization for the spatial fractional Riesz derivative, a …

A novel energy-stable scheme is proposed to solve the spatial fractional Cahn–Hilliard
equations, using the idea of scalar auxiliary variable (SAV) approach and stabilization …