Numerical Methods for Solving the Multi-term Time-fractional Wave-diffusion Equation.


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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@article{Liu2013NumericalMF, title={Numerical Methods for Solving the Multi-term Time-fractional Wave-diffusion Equation.}, author={Frank Liu and Mark M. Meerschaert and Robert J. McGough and Philip Zhuang and Q Liu}, journal={Fractional calculus & applied analysis}, year={2013}, volume={16 1}, pages={9-25} }