A new fully discrete finite difference/element approximation for fractional cable equation

被引：29
作者：
Liu J. [1 ]
Li H. [1 ]
Liu Y. [1 ]
机构：
[1] School of Mathematical Sciences, Inner Mongolia University, Hohhot
来源：
Journal of Applied Mathematics and Computing | 2016年 / 52卷 / 1-2期
基金：
中国国家自然科学基金;
关键词：
Error estimate; Finite difference method; Finite element method; Fractional cable equation; Novel discrete scheme; Stability;
D O I：
10.1007/s12190-015-0944-0
中图分类号：
学科分类号：
摘要：
A novel fully discrete Crank–Nicolson finite element method, which is obtained by finite difference in time and finite element in space, is presented to approximate the fractional Cable equation. Compared to the L1-formula for discretizing fractional derivatives at time tn+1, the proposed approximate scheme is directly obtained at time tn+12, in which some new coefficients (k+12)1-α-(k-12)1-α instead of (k+ 1) 1-α- k1-α are derived. Based on the new approximate formula, the stability and error estimate are analyzed in detail and the optimal convergence rate O(τmin{1+α1,1+α2}+hr+1) is obtained. Numerical examples in one-dimensional and two-dimensional spaces are shown to illustrate the effectiveness and feasibility of the studied algorithm. © 2015, Korean Society for Computational and Applied Mathematics.
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页码：345 / 361
页数：16
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