A weighted and shifted difference formula is constructed based on the Lubich operators,
which gives a forth-order and unconditionally stable difference scheme for the Cauchy …

In this article, a compact difference method is proposed for fractional viscoelastic beam
vibration in stress-displacement form. The solvability, the unconditional stability and the …

The convergence of a compact finite difference scheme for one-and twodimensional time
fractional fourth order equations with the first Dirichlet boundary conditions is studied. In one …

In this paper, we propose an improved finite difference/finite element method for the
fractional Rayleigh–Stokes problem with a nonlinear source term. The second-order …

In this paper, two linearized Galerkin finite element methods, which are based on the L 1
approximation and the WSGD operator, respectively, are proposed to solve the nonlinear …

A conservative finite difference scheme for nonlinear space fractional Klein-Gordon-
Schrödinger systems with high-degree Yukawa interaction is studied. We show that the …

In the present paper, the semilinear integro-differential diffusion equation and system with
singular in time sources are considered. An analog of Duhamel's principle for the linear …

In this paper, we present an efficient linearized alternating direction implicit (ADI) scheme for
two-dimensional time-space fractional nonlinear diffusion-wave equations with initial …

This paper presents a second-order linearized finite difference scheme for the nonlinear
time-fractional fourth-order reaction-diffusion equation. The temporal Caputo derivative is …

This paper presents a linearized finite difference scheme for solving a kind of time-space
fractional nonlinear diffusion-wave equations with initial singularity, where the Caputo …