title: NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.
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.
authors.affiliation: School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia.
authors.forename: F
authors.initials: F
authors.lastname: Liu
authors.forename: M M
authors.initials: MM
authors.lastname: Meerschaert
authors.forename: R J
authors.initials: RJ
authors.lastname: McGough
authors.forename: P
authors.initials: P
authors.lastname: Zhuang
authors.forename: Q
authors.initials: Q
authors.lastname: Liu
keywords: Caputo derivative; a power law wave equation; finite difference method; fractional predictor-corrector method; multi-term time fractional wave-diffusion equations