Some second-order θ schemes combined with finite element method for nonlinear fractional cable equation

被引：81
|
作者：
Liu, Yang [1 ]
Du, Yanwei [1 ,3 ]
Li, Hong [1 ]
Liu, Fawang [2 ]
Wang, Yajun [1 ]
机构：
[1] Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China
[2] Queensland Univ Technol, Sch Math Sci, GPO Box 2434, Brisbane, Qld 4001, Australia
[3] Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China
来源：
NUMERICAL ALGORITHMS | 2019年 / 80卷 / 02期
基金：
澳大利亚研究理事会;
关键词：
Second-order theta scheme; Nonlinear fractional cable equation; Finite element algorithm; Stability; Error estimates; DISCONTINUOUS GALERKIN METHOD; DIFFERENCE APPROXIMATIONS; SUBDIFFUSION;
D O I：
10.1007/s11075-018-0496-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, some second-order time discrete schemes covering parameter ? combined with Galerkin finite element (FE) method are proposed and analyzed for looking for the numerical solution of nonlinear cable equation with time fractional derivative. At time t(k-?), some second-order ? schemes combined with weighted and shifted Grunwald difference (WSGD) approximation of fractional derivative are considered to approximate the time direction, and the Galerkin FE method is used to discretize the space direction. The stability of second-order ? schemes is derived and the second-order time convergence rate in L-2-norm is proved. Finally, some numerical calculations are implemented to indicate the feasibility and effectiveness for our schemes.
引用
收藏
页码：533 / 555
页数：23
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