In this article, a second-order-accuracy algorithm is proposed for solving time-space
fractional heat equations (TSFHEs) in one and two dimensions. The new algorithm …

Convection-diffusion problems, due to its fundamental nature, are found in various science
and engineering applications. In this research, the importance of the relationship between …

In this paper, we propose an alternating direction implicit (ADI) difference method to solve
the two-dimensional time-fractional reaction-subdiffusion equation with weakly singular …

In this paper, we consider a fast second-order implicit difference method to approximate a
class of linear time-space fractional variable coefficients advection-diffusion equation. To …

The scalar convection-dominated flows are found in different science and designing
applications which incorporates those concerning the computational fluid dynamics …

This study presents a novel high-order numerical method designed for solving the two-
dimensional time-fractional convection-diffusion (TFCD) equation. The Caputo definition is …

Based on the idea of operator splitting, this paper proposes two efficient operator splitting
schemes for the Allen-Cahn equation. The original equation is divided into linear and …

A high-order Crank-Nicolson-type compact difference method is proposed for a class of time
fractional Cattaneo convection-diffusion equations with smooth solutions. The convection …

本文基于算子分裂方法, 提出了求解分数阶Gray-Scott 模型的一种高效数值逼近格式.
首先采用算子分裂法将原问题分解为线性子问题和非线性子问题: 线性子问题采用Crank …

A high-order finite difference numerical scheme based on the compact difference operator is
proposed in this paper for time-fractional partial integro-differential equations with a weakly …