Recent advances in improving the computational efficiency of the phase-field simulations of
solidification microstructures are reviewed. The parallel progress of four typical approaches …

We study (time) fractional Allen–Cahn and Cahn–Hilliard phase-field models to account for
the anomalously subdiffusive transport behavior in heterogeneous porous materials or …

In the paper, a Crank–Nicolson alternating direction implicit (ADI) Galerkin–Legendre
spectral scheme is presented for the two-dimensional Riesz space distributed-order …

The main aim of the current paper is to propose an efficient numerical technique for solving
two-dimensional space-multi-time fractional Bloch–Torrey equations. The current research …

An efficient numerical technique is proposed to solve one-and two-dimensional space
fractional tempered fractional diffusion-wave equations. The space fractional is based on the …

The phase-field crystal equation is a sixth-order nonlinear parabolic equation and can be
applied to simulate various phenomena such as epitaxial growth, material hardness, and …

This paper introduces a high-order numerical procedure to solve the two-dimensional
distributed-order Riesz space-fractional diffusion equation. In the proposed technique, first, a …

In this paper, we study space fractional Cahn-Hilliard equations. A second-order stabilized
finite difference scheme is exploited for the model equations. The resulting coefficient matrix …

In this paper, we develop an unconditionally stable linear numerical scheme for the N-
component Cahn–Hilliard system with second-order accuracy in time and space. The …

In the current investigation, an error estimate has been proposed to solve the two-
dimensional weakly singular integro-partial differential equation with space and time …