时间分数阶扩散方程的并行高效Legendre谱方法  

A parallel and efficient Legendre spectral method for time-fractional diffusion equations

作　　者：陈红斌[1] 马甲迎[1] 刘晓奇[1] 

机构地区：[1]中南林业科技大学理学院数学物理研究所,湖南长沙410004

出　　处：《中南林业科技大学学报》2011年第1期148-152,共5页Journal of Central South University of Forestry & Technology

基　　金：国家自然科学基金(10971062);湖南省高等学校科学研究基金(07C805);中南林业科技大学青年科学研究基金重点项目(2008002A)

摘　　要：研究了两类时间分数阶扩散方程的并行高效Legendre谱方法,分数阶导数分别代替标准的扩散方程的二阶空间导数和一阶时间导数。空间方向采用高效的Legendre谱方法,时间方向使用了基于Fourier级数展开的Laplace数值逆,并对其参数进行了优化。给出了两类时间分数阶扩散程的数值格式和数值例子,与其他方法比,该方法数值结果更优。A parallel and efficient Legendre spectral method for two time-fractional diffusion equations was considered,in which one was obtained from the standard diffusion equation by replacing the second-order space derivative with a fractional derivative,while the other was obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative.Efficient Legendre Spectral scheme was adopted in space;the numerical inversion of Laplace transforms based on Fourier series expansion was used in time and an optimal model to determine the free parameter was constructed.Numerical experiments were given to demonstrate its efficiency.

关 键 词：时间分数阶扩散方程 LEGENDRE谱方法 Fourier级数展开 Laplace数值逆 参数优化 数值例子 

分 类 号：O175[理学—数学]