Numerical Methods for Solving the Multi-Term Time-Fractional Wave-Diffusion Equations

摘要

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multiterm time fractional derivatives are de.ned 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 e.ective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the e.ectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional timespace models with fractional Laplacian.