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

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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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DOI: https://doi.org/10.1007/s12190-020-01449-x