Related papers: Spatial two-grid compact difference scheme for two…
In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation…
The aim of this paper is to develop fast second-order accurate difference schemes for solving one- and two-dimensional time distributed-order and Riesz space fractional diffusion equations. We adopt the same measures for one- and…
In this work, a second-order approximation of the fractional substantial derivative is presented by considering a modified shifted substantial Gr\"{u}nwald formula and its asymptotic expansion. Moreover, the proposed approximation is…
The numerical analysis of time fractional evolution equations with the second-order elliptic operator including general time-space dependent variable coefficients is challenging, especially when the classical weak initial singularities are…
Based on the weighted and shifted Gr\"{u}nwald difference (WSGD) operators [24], we further construct the compact finite difference discretizations for the fractional operators. Then the discretization schemes are used to approximate the…
The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discrete scheme via using the linear finite element method to…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
Propagation characteristics of a wave are defined by the dispersion relationship, from which the governing partial differential equation (PDE) can be recovered. PDEs are commonly solved numerically using the finite-difference (FD) method,…
Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…
A kind of spatial fractional diffusion equations in this paper are studied. Firstly, an L1 formula is employed for the spatial discretization of the equations. Then, a second order scheme is derived based on the resulting semi-discrete…
An implicit finite difference scheme based on the $L2$-$1_{\sigma}$ formula is presented for a class of one-dimensional time fractional reaction-diffusion equations with variable coefficients and time drift term. The unconditional stability…
Efficient and accurate numerical simulation of 3D acoustic wave propagation in heterogeneous media plays an important role in the success of seismic full waveform inversion (FWI) problem. In this work, we employed the combined scheme and…
This paper presents a novel and straightforward compact reconstruction procedure for the high-order finite volume method on unstructured grids. In this procedure, we constructed a linear approximation relationship between the mean values…
In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To start with, an implicit difference method based on two-sided…
Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a…
The speed of sound in two-phase pipe flow systems is often several orders of magnitude greater than the travelling speed of hydraulic information (volume fractions.) Dynamically simulating such flows requires resolution of acoustic and…
We consider a nonlinear mixed-dimensional model for simulating gas transport in shale formation. The mathematical model consists of a coupled system of nonlinear equations, where flow within fractures is represented using a…
Calculating dynamical diffraction patterns for X-ray topography and similar x-ray scattering-imaging techniques require the numerical integration of the Takagi-Taupin equations. This is usually performed with a simple second order finite…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the…