This paper has presented a new semi-analytic numerical method for solving multi-point
problems for nonlinear singular ordinary differential equations (ODEs) of a high order. The …

An implicit variable-step BDF2 scheme is established for solving the space fractional Cahn-
Hilliard equation, involving the fractional Laplacian, derived from a gradient flow in the …

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 …

An implicit variable-step BDF2 scheme is established for solving the space fractional Cahn-
Hilliard equation derived from a gradient flow in the negative order Sobolev space H-α …

The phenomena of non-locality and spatial heterogeneity are intricate, and using fractional
differential equations provides a robust modeling approach for understanding these …

In this paper, an efficient finite difference scheme is developed for solving the time-fractional
Cahn–Hilliard equations which is the well-known representative of phase-field models. The …

We extend the classical Allen–Cahn (AC) equation to the fractional Allen–Cahn equation
(FAC) with triple-well potential. By replacing the spatial Laplacian and double-well potential …

In the paper, the symplectic‐preserving Fourier spectral scheme is presented for space
fractional Klein–Gordon–Schrödinger equations involving fractional Laplacian. First, we …

In this study, we focus on two fractional conservative Allen–Cahn equations with a nonlocal
space-independent operator (called the RSLM operator) and a local-nonlocal space–time …

In this study, we consider volume-conserved numerical schemes for the volume-conserved
time fractional Allen-Cahn equation. We start with the L1 scheme based on a modified …