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Two linearized schemes for time fractional nonlinear wave equations with fourth-order derivative

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Abstract

In this paper, two linearized schemes for time fractional nonlinear wave equations (TFNWEs) with the space fourth-order derivative are proposed and analyzed. To reduce the smoothness requirement in time, the considered TFNWEs are equivalently transformed into their partial integro-differential forms by the Riemann–Liouville integral. Then, the first scheme is constructed by using piecewise rectangular formulas in time and the fourth-order approximation in space. And, this scheme can be fast evaluated by the sum-of-exponentials technique. The second scheme is developed by using the Crank–Nicolson technique combined with the second-order convolution quadrature formula. By the energy method, the convergence and unconditional stability of the proposed schemes are proved rigorously. Finally, numerical experiments are given to support our theoretical results.

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Acknowledgements

This research is supported by National Natural Science Foundation of China (Grant Nos. 11701502 and 11871065).

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Authors and Affiliations

  1. College of Mathematical Sciences, Yangzhou University, Yangzhou, 225002, China

    Jianfei Huang, Zhi Qiao & Jingna Zhang

  2. COMSATS University Islamabad, Lahore Campus, Islamabad, Pakistan

    Sadia Arshad

  3. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yifa Tang

  4. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Yifa Tang

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  1. Jianfei Huang
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Correspondence to Jianfei Huang.

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Huang, J., Qiao, Z., Zhang, J. et al. Two linearized schemes for time fractional nonlinear wave equations with fourth-order derivative. J. Appl. Math. Comput. 66, 561–579 (2021). https://doi.org/10.1007/s12190-020-01449-x

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