检索结果-南通市图书馆

Analysis of an Implicit Finite Difference Scheme for time fractional diffusion equation

Chinese Quarterly Journal of Mathematics 2016年第1期31卷 69-81页

作者： MA Yan College of Technology and Engineering Lanzhou University of Technology

time fractional diffusion equation is usually used to describe the problems involving non-Markovian random walks. This kind of equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α∈(0, 1). In this paper, an implicit finite difference scheme for solving the time fractional diffusion equation with source term is presented and analyzed, where the fractional derivative is described in the Caputo sense. Stability and convergence of this scheme are rigorously established by a Fourier analysis. And using numerical experiments illustrates the accuracy and effectiveness of the scheme mentioned in this paper.

关键词： time fractional diffusion equation finite difference approximation implicit scheme stability convergence effectiveness

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

A DIRECT DISCONTINUOUS GALERKIN METHOD FOR time fractional diffusion equationS WITH fractional DYNAMIC BOUNDARY CONDITIONS

引用

Journal of Computational Mathematics 2024年第1期42卷 156-177页

作者： Jingjun Zhao Wenjiao Zhao Yang Xu School of Mathematics Harbin Institute of TechnologyHarbin 150001China

This paper deals with the numerical approximation for the time fractional diffusion problem with fractional dynamic boundary *** well-posedness for the weak solutions is studied.A direct discontinuous Galerkin approach is used in spatial direction under the uniform meshes,together with a second-order Alikhanov scheme is utilized in temporal direction on the graded mesh,and then the fully discrete scheme is ***,the stability and the error estimate for the full scheme are analyzed in *** experiments are also given to illustrate the effectiveness of the proposed method.

关键词： time fractional diffusion equation Numerical stability Convergence

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Spectral Optimization Methods for the time fractional diffusion Inverse Problem

引用

Numerical Mathematics(Theory,Methods and Applications) 2013年第3期6卷 499-519页

作者： Xingyang Ye Chuanju Xu School of Mathematical Sciences Xiamen UniversityXiamen 361005FujianChina School of Science Jimei UniversityXiamen 361021FujianChina

An inverse problem of reconstructing the initial condition for a time fractional diffusion equation is *** the basis of the optimal control framework,the uniqueness and first order necessary optimality condition of the minimizer for the objective functional are established,and a time-space spectral method is proposed to numerically solve the resulting minimization *** contribution of the paper is threefold:1)a priori error estimate for the spectral approximation is derived;2)a conjugate gradient optimization algorithm is designed to efficiently solve the inverse problem;3)some numerical experiments are carried out to show that the proposed method is capable to find out the optimal initial condition,and that the convergence rate of the method is exponential if the optimal initial condition is smooth.

关键词： time fractional diffusion equation inverse problem spectral method error estimate conjugate gradient method.

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Application of low-dimensional finite element method to fractional diffusion equation

引用

International Journal of Modeling, Simulation, and Scientific Computing 2014年第4期5卷 184-200页

作者： Jincun Liu Hong Li Zhichao Fang Yang Liu School of Mathematical Sciences Inner Mongolia University Hohhot 010021 P.R.China

Classical finite element method(FEM)has been applied to solve some fractional differential equations,but its scheme has too many degrees of *** this paper,a low-dimensional FEM,whose number of basis functions is reduced by the theory of proper orthogonal decomposition(POD)technique,is proposed for the time fractional diffusion equation in two-dimensional *** presented method has the properties of low dimensions and high accuracy so that the amount of computation is decreased and the calculation time is ***,error estimation of the method is *** example is given to illustrate the feasibility and validity of the low-dimensional FEM in comparison with traditional FEM for the time fractional differential equations.

关键词： Low-dimensional finite element method proper orthogonal decomposition time fractional diffusion equation error estimation

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

欢迎您,

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

在线全文

在线全文

在线全文

请选择保存的检索档案：

请选择收藏分类：

通借通还

欢迎您,

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

在线全文

在线全文

在线全文

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：