We develop a fractional extension of a mass-conserving Allen–Cahn phase field model that
describes the mixture of two incompressible fluids. The fractional order controls the …

We consider a fractional Laplacian defined in bounded domains by the eigen-
decomposition of the integer-order Laplacian, and demonstrate how to compute very …

A numerical method for a kind of time-dependent two-dimensional two-sided space
fractional diffusion equations is developed in this paper. The proposed method combines a …

A novel Douglas alternating direction implicit (ADI) method is proposed in this work to solve
a two-dimensional (2D) heat equation with interfaces. The ADI scheme is a powerful finite …

In this paper, we propose a second-order operator splitting spectral element method for
solving fractional reaction-diffusion equations. In order to achieve a fast second-order …

The paper proposes and examines the stability and convergence properties of an extension
of the direction splitting methods towards parabolic and incompressible flow problems in …

A fully higher-order compact (HOC) finite difference scheme on the 9-point two-dimensional
(2D) stencil is formulated for solving the steady-state laminar mixed convection flow in a lid …

An efficient parallel algorithm for the time dependent incompressible Navier–Stokes
equations is developed in this paper. The time discretization is based on a direction splitting …