Finite element method combined with second-order time discrete scheme for nonlinear fractional Cable equation

被引：27
|
作者：
Wang, Yajun [1 ]
Liu, Yang [1 ]
Li, Hong [1 ]
Wang, Jinfeng [1 ,2 ]
机构：
[1] Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China
[2] Inner Mongolia Univ Finance & Econ, Sch Math & Stat, Hohhot 010070, Peoples R China
来源：
EUROPEAN PHYSICAL JOURNAL PLUS | 2016年 / 131卷 / 03期
关键词：
DISCONTINUOUS GALERKIN METHOD; DIFFERENCE METHOD; NUMERICAL-METHODS; ANOMALOUS-DIFFUSION; SUBDIFFUSION; APPROXIMATIONS; CONVERGENCE; STABILITY;
D O I：
10.1140/epjp/i2016-16061-3
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this article, a Galerkin finite element method combined with second-order time discrete scheme for finding the numerical solution of nonlinear time fractional Cable equation is studied and discussed. At time , a second-order two step scheme with -parameter is proposed to approximate the first-order derivative, and a weighted discrete scheme covering second-order approximation is used to approximate the Riemann-Liouville fractional derivative, where the approximate order is higher than the obtained results by the L1-approximation with order ( in the existing references. For the spatial direction, Galerkin finite element approximation is presented. The stability of scheme and the rate of convergence in -norm with are derived in detail. Moreover, some numerical tests are shown to support our theoretical results.
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收藏
页数：16
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