What question did this study set out to answer?

The aim is to develop numerical schemes that maintain energy stability and the maximum bound principle while achieving temporal accuracy for ternary Allen-Cahn equations.

July 12, 2026Advances in Continuous and Discrete ModelsOpen Access

Some maximum bound principle preserving and energy stable exponential time differencing Runge-Kutta schemes for ternary Allen-Cahn equations

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Authors

XWXinyang WuBeihua University HCHongbo ChenGuangxi University ZWZian WangUniversity of Waterloo

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Implication

Randomized trial demonstrates improved accuracy in energy stability and maximum bound principle for ternary Allen-Cahn equations, indicating robust numerical methods.

Key Points

The aim is to develop numerical schemes that maintain energy stability and the maximum bound principle while achieving temporal accuracy for ternary Allen-Cahn equations.
Developed first- and second-order numerical schemes using exponential time differencing Runge-Kutta (ETDRK) methods.
Proved unconditional preservation of the initial energy decreasing property and maximum bound principle for the equations.
Established a maximum-norm error estimate based on the maximum bound principle.
The proposed ETDRK schemes successfully preserved the initial energy decreasing property with a first-order accuracy.
Energy stability and maximum bound principle were guaranteed in all numerical experiments conducted.
Numerical experiments confirmed the effectiveness of the proposed schemes compared to previous methods.

Cite This Study

Wu et al. (2026) studied this question.

synapsesocial.com/papers/6a53315f4f7abc118aded892 https://doi.org/10.1186/s13662-026-04117-9

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Implication

Randomized trial demonstrates improved accuracy in energy stability and maximum bound principle for ternary Allen-Cahn equations, indicating robust numerical methods.

Some maximum bound principle preserving and energy stable exponential time differencing Runge-Kutta schemes for ternary Allen-Cahn equations

Discussion

Member takes

Implication

Key Points

Cite This Study

Some maximum bound principle preserving and energy stable exponential time differencing Runge-Kutta schemes for ternary Allen-Cahn equations

Discussion

Member takes

Implication

Key Points

Cite This Study

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