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Energy Stability of Adaptive Exponential Time Difference Runge-Kutta Method (ETDRK32)

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Abstract

The Exponential Time Difference Runge–Kutta method (ETDRK) is an important approach for simulating gradient flow models, and whether it can maintain energy stability is an important research topic. New adaptive ETDRK method (ETDRK32) has been designed in [4] and proven to possess the property of long time unconditional energy stability for one specific parameter \(\alpha =\frac{2}{3}\). In this paper, we adopt a new method of semi-positive definite matrix decomposition to prove the long-term energy stability of the schemes when the parameter \(\alpha \) is within a certain range. Furthermore, we provide numerical simulations to verify the theoretical analysis and demonstrate the convergence and energy stability of the new schemes.

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Acknowledgements

Chen is supported by the National Natural Science Foundation of China (NSFC 12471369 and NSFC 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 for their constructive comments and suggestions which led to an improved presentation of this paper.

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  1. Weichen Cao

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

Authors and Affiliations

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

    Hengli Yang & Weichen Cao

  2. 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. Hengli Yang
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Correspondence to Wenbin Chen.

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Yang, H., Cao, W. & Chen, W. Energy Stability of Adaptive Exponential Time Difference Runge-Kutta Method (ETDRK32). J Sci Comput 103, 28 (2025). https://doi.org/10.1007/s10915-025-02840-1

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