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A high-efficiency second-order numerical scheme for time-fractional phase field models by using extended SAV method

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Abstract

In this paper, a second-order numerical scheme for the time-fractional phase field models is proposed. In this scheme, the fractional backward difference formula is used to approximate the time-fractional derivative and the extended scalar auxiliary variable method is used to deal with the nonlinear terms. The energy dissipation property for the numerical scheme is proved. Our discussion includes the time-fractional Allen–Cahn equation, the time-fractional Cahn–Hilliard equation, and the time-fractional molecular beam epitaxy model. In the numerical implementation, a fast method based on a globally uniform approximation of the trapezoidal rule for the integral on the real line is adopted to decrease the memory requirement and computational cost. Finally, some numerical examples are given to confirm the effectiveness of the proposed methods.

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Acknowledgements

We would like to express our gratitude to the Editor for taking time to handle the manuscript. This work has been supported by the National Natural Science Foundation of China (Grants Nos. 11771254, 11672163), Major Basic Research Projects of Natural Science Foundation of Shandong Province (Grants No. ZR2019ZD42), and Natural Postdoctoral Innovative Talents Support Program (Grant No. BX20190191).

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  1. School of Mathematics, Shandong University, Jinan, 250100, People’s Republic of China

    Hui Zhang & Xiaoyun Jiang

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  1. Hui Zhang
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Correspondence to Xiaoyun Jiang.

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Zhang, H., Jiang, X. A high-efficiency second-order numerical scheme for time-fractional phase field models by using extended SAV method . Nonlinear Dyn 102, 589–603 (2020). https://doi.org/10.1007/s11071-020-05943-6

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