A numerical method and its fast implementation for multi-term fractional nonlinear wave equations

doi:10.3969/j.issn.1000-1565.2022.05.002

Abstract

Abstract: A linearized numerical method for multi-term time fractional nonlinear wave equations with a spatial fourth-order derivative is derived. To avoid solving the nonlinear system of equations, a linearized technique is applied to discretize the nonlinear term. Then, the convergence of this presented method is rigorously proved with the first-order accuracy in time and the fourth-order accuracy in space. It is worth mentioning that the presented method can handle the initial singularity, and can be fast calculated by the sum-of-exponentials technique. Finally, numerical experiments are given to verify the effectiveness of this method and the correctness of the theoretical results.

Key words: multi-term fractional wave equations, fourth-order derivative, numerical method, convergence, fast implementation

CLC Number:

O241.82

SHAO Linxin, SHEN Zhuoyang, MA Geqinzhou, MIN Jie, HUANG Jianfei. A numerical method and its fast implementation for multi-term fractional nonlinear wave equations[J]. Journal of Hebei University(Natural Science Edition), 2022, 42(5): 454-462.

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