Numerical methods for solving the multi-term time-fractional wave-diffusion equation

被引：296
|
作者：
Liu, Fawang [1 ]
Meerschaert, Mark M. [2 ]
McGough, Robert J. [3 ]
Zhuang, Pinghui [4 ]
Liu, Qingxia [4 ]
机构：
[1] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
[2] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA
[3] Michigan State Univ, Dept Elect & Comp Engn, E Lansing, MI 48824 USA
[4] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2013年 / 16卷 / 01期
基金：
澳大利亚研究理事会;
关键词：
multi-term time fractional wave-diffusion equations; Caputo derivative; a power law wave equation; finite difference method; fractional predictor-corrector method; FREQUENCY POWER-LAW; ANOMALOUS SUBDIFFUSION EQUATION; NONLINEAR SOURCE-TERM; DOMAIN; MEDIA; APPROXIMATIONS; STABILITY; MODELS;
D O I：
10.2478/s13540-013-0002-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.
引用
收藏
页码：9 / 25
页数：17
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