Efficient and stable numerical methods for the two-dimensional fractional Cattaneo equation

被引：16

作者：

Ren, Jincheng ^{[1
]}

Gao, Guang-hua ^{[2
]}

机构：

[1] Henan Univ Econ & Law, Coll Math & Informat Sci, Zhengzhou 450000, Peoples R China

[2] Nanjing Univ Posts & Telecommun, Coll Sci, Nanjing 210046, Jiangsu, Peoples R China

来源：

NUMERICAL ALGORITHMS | 2015年 / 69卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Fractional cattaneo equation; Compact ADI difference scheme; ADI scheme; Discrete energy method; Stability; Convergence; ANOMALOUS DIFFUSION; RANDOM-WALKS; CALCULUS;

D O I：

10.1007/s11075-014-9926-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

New numerical methods are presented for the solution of a two-dimensional Cattaneo equation with the time fractional derivative. A difference scheme combining the compact difference approach for the spatial discretization and alternating direction implicit (ADI) method in the time stepping is proposed and analyzed. The compact ADI scheme is constructed by adding a small term, the unconditional stability and the global convergence of the scheme are proved rigorously. In addition, an ADI scheme is presented and the corresponding error estimate is also established. Numerical experiments are included to support the theoretical results, and the comparison with the ADI scheme is presented to show the effectiveness of the compact ADI scheme.

引用

页码：795 / 818

页数：24

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