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An Exponential Time Differencing Runge–Kutta Method ETDRK32 for Phase Field Models

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Abstract

The exponential time differencing Runge–Kutta method (ETDRK) developed by Cox and Matthews has proven effective in computing nonlinear partial differential equation. However, it is difficult to prove the unconditional energy stability for third-order or higher ETDRK method. In this paper, we proposed a new third-order ETDRK scheme, ETDRK3, and prove its unconditional energy stability. Combining ETDRK3 with a second-order scheme ETDRK2, we proposed an adaptive ETDRK method(ETDRK32). Furthermore, the numerical simulations for phase problems demonstrate the accuracy, stability and efficiency of adaptive step-size strategy.

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Acknowledgements

Chen is supported by the National Natural Science Foundation of China (NSFC) 12241101 and 12071090, he also thanks the Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, for the support. Finally, we are greatly indebted to the referees their constructive comments and suggestions which led to an improved presentation of this paper.

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  1. Hengli Yang

    Present address: Academy for Engineering and Technology, Fudan University, Shanghai, 200433, People’s Republic of China

Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Weichen Cao

  2. Academy for Engineering and Technology, Fudan University, Shanghai, 200433, People’s Republic of China

    Weichen Cao

  3. School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China

    Wenbin Chen

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  1. Weichen Cao
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Correspondence to Wenbin Chen.

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Cao, W., Yang, H. & Chen, W. An Exponential Time Differencing Runge–Kutta Method ETDRK32 for Phase Field Models. J Sci Comput 99, 6 (2024). https://doi.org/10.1007/s10915-024-02474-9

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