Liu F, Meerschaert M, McGough R, Zhuang P, Liu Q. NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.
FRACTIONAL CALCULUS & APPLIED ANALYSIS 2013;
16:9-25. [PMID:
23772179 PMCID:
PMC3679177 DOI:
10.2478/s13540-013-0002-2]
[Citation(s) in RCA: 224] [Impact Index Per Article: 20.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2012] [Indexed: 11/20/2022]
Abstract
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.
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