Related papers: Fourier spectral approximation for the convective …
In this paper, we study a second-order accurate and linear numerical scheme for the nonlocal Cahn-Hilliard equation. The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for…
The Cahn-Hilliard equation is a fundamental model for describing phase separation phenomena in binary mixtures. Traditional numerical methods, such as finite difference and finite element methods, often incur substantial computational cost,…
In this article, we consider the stochastic Cahn--Hilliard equation driven by multiplicative space-time white noise with diffusion coefficient of sublinear growth. By introducing the spectral Galerkin method, we first obtain the…
We develop a decoupled, first-order, fully discrete, energy-stable scheme for the Cahn-Hilliard-Navier-Stokes equations. This scheme calculates the Cahn-Hilliard and Navier-Stokes equations separately, thus effectively decoupling the entire…
In this paper, we propose, analyze and implement efficient time parallel methods for the Cahn-Hilliard (CH) equation. It is of great importance to develop efficient numerical methods for the CH equation, given the range of applicability of…
Anomalous diffusions are ubiquitous in nature, whose functional distributions are governed by the backward Feynman-Kac equation. In this paper, the local discontinuous Galerkin (LDG) method is used to solve the 2D backward Feynman-Kac…
We solve the Cauchy problem of the Ward model in light-cone coordinates using the inverse spectral (scattering) method. In particular we show that the solution can be constructed by solving a $2\times 2$ local matrix Riemann-Hilbert problem…
We present a concise report on the '2DHybrid' method, an innovative extension of two-dimensional correlation spectroscopy (2D COS), tailored for quasar light curve analysis. Addressing the challenge of discerning periodic variations against…
We extensively study the numerical accuracy of the well-known time splitting Fourier spectral method for the approximation of singular solutions of the Gross-Pitaevskii equation. In particular, we explore its capability of preserving a…
We apply the semi-discrete method, c.f. \emph{N. Halidias and I.S. Stamatiou (2016), On the numerical solution of some non-linear stochastic differential equations using the semi-discrete method, Computational Methods in Applied…
We propose the functions defined by the maximum of a discrete quadratic form and satisfying the ultradiscrete KdV equation. These functions includes not only soliton solutions but also pseudo-periodic solutions. In the proof, we employ some…
A high-order numerical method is developed for solving the Cahn-Hilliard-Navier-Stokes equations with the Flory-Huggins potential. The scheme is based on the $Q_k$ finite element with mass lumping on rectangular grids, the second-order…
Geometric discretizations that preserve certain Hamiltonian structures at the discrete level has been proven to enhance the accuracy of numerical schemes. In particular, numerous symplectic and multi-symplectic schemes have been proposed to…
In this paper, we propose a linearized Fourier pseudo-spectral method, which preserves the total mass and energy conservation laws, for the damped nonlinear Schr\"{o}dinger equation in three dimensions. With the aid of the semi-norm…
A finite difference numerical scheme is proposed and analyzed for the Cahn-Hilliard-Stokes system with Flory-Huggins energy functional. A convex splitting is applied to the chemical potential, which in turns leads to the implicit treatment…
The Allen-Cahn equation is solved numerically by operator splitting Fourier spectral methods. The basic idea of the operator splitting method is to decompose the original problem into sub-equations and compose the approximate solution of…
We propose and analyze a first-order finite difference scheme for the functionalized Cahn-Hilliard (FCH) equation with a logarithmic Flory-Huggins potential. The semi-implicit numerical scheme is designed based on a suitable convex-concave…
This paper discusses the spectral collocation method for numerically solving nonlocal problems: one dimensional space fractional advection-diffusion equation; and two dimensional linear/nonlinear space fractional advection-diffusion…
We obtain necessary conditions and sufficient conditions on the existence of solutions to the Cauchy problem for a fractional semilinear heat equation with an inhomogeneous term. We identify the strongest spatial singularity of the…
Numerical solution of one-dimensional stochastic integral equations because of the randomness has its own problems, i.e. some of them no have analytically solution or finding their analytic solution is very difficult. This problem for…