时间分数阶慢扩散方程的谱方法  

A discrete spectral method for the time fractional sub-diffusion equation

作　　者：赵小明 吕淑娟[1] ZHAO Xiaoming;Lu Shujuan(School of Mathematics and Systems Science,Beihang University,Beijing 100191,China)

机构地区：[1]北京航空航天大学数学与系统科学学院,北京100191

出　　处：《黑龙江大学自然科学学报》2018年第6期631-638,共8页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11672011;11272024)

摘　　要：用加权移位的三阶Grünwald差分(WSGD)算子逼近时间分数阶导数,空间方向上采用Legendre谱方法,对时间分数阶慢扩散方程构造了全离散格式。用能量方法证明格式的稳定性,用误差估计方法证明格式的收敛性,得到收敛阶为O(τ3+N-m)。数值实验验证了算法的有效性和理论结果的正确性。By using the third-order weighted shifted Grünwald difference( WSGD) operator in time and the Legendre spectral method in space,a fully discrete scheme is constructed for the time fractional subdiffusion equation. The stability is proved by the energy method. The convergence is proved by the error estimation,and the convergence order is O( τ3+ N-m). The effectiveness of algorithm and correction of results is illustrated by the numerical example.

关 键 词：时间分数阶慢扩散方程 LEGENDRE谱方法 WSGD算子 稳定性 收敛性 

分 类 号：O241.82[理学—计算数学]