Multi-dimensional space-fractional diffusion equation with variable coefficients and fractional gradient is a difficult problem in theory and computation. As far as we know, there rarely exist well-posedness results and efficient numerical approaches for such equation. In this paper, we focus on this...
In this paper a Riesz space fractional diffusion equation on a finite domain is considered. 在有限区域内考虑具有初边值问题的Riesz空间分数阶扩散方程,传统扩散方程中的二阶空间导数由Riesz分数阶导数α(1<α≤2)代替就得到Riesz空间分数阶扩散方程。2...
In this paper a Riesz space fractional diffusion equation on a finite domain is considered. 在有限区域内考虑具有初边值问题的Riesz空间分数阶扩散方程,传统扩散方程中的二阶空间导数由Riesz分数阶导数α(1<α≤2)代替就得到Riesz空间分数阶扩散方程。6...
In this paper, the multi-term time-space fractional diffusion equation with fractional boundary conditions is considered. The fractional derivative in space is approximated by the standard and shiftedGru篓nwald-Letnikov\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\use...
In this paper, a compact difference operator, termed CWSGD, is designed to establish the quasi-compact finite difference schemes for approximating the space fractional diffusion equations in one and two dimensions. The method improves the spatial accuracy order of the weighted and shifted Grünwald di...
Approximating Riesz space fractional diffusion equation in time by k-step backward difference formula and in space by spectral Galerkin method, we establish a fully discrete scheme with high order both in time and in space. For k <= 5, we prove the stability of full discretization and obtain ...
Time-space fractional diffusion equationFractional differential equations are powerful tools to model the non-locality and spatial heterogeneity evident in many real-world problems. Although numerous numerical methods have been proposed, most of them are limited to regular domains and uniform meshes. For...
Firstly, we present the finite volume scheme for the two-dimensional space fractional diffusion equation with variable coefficients and provide the full implementation details for the case where the background interpolation mesh is based on triangular elements. Secondly, we explore the property of the ...
5) Riesz space fractional diffusion equation 空间分数阶扩散方程 1. In this paper a Riesz space fractional diffusion equation on a finite domain is considered. 在有限区域内考虑具有初边值问题的Riesz空间分数阶扩散方程,传统扩散方程中的二阶空间导数由Riesz分数阶导数α(1<α≤2)代替就得到Riesz空间...
In this paper, a compact alternating direction implicit (ADI) method has been developed for solving two-dimensional Riesz space fractional diffusion equation. The precision of the discretization method used in spatial directions is twice the order of the corresponding fractional derivatives. It is prove...