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High-order, linearly implicit, and energy-stable methods for Cahn–Hilliard models with degenerate mobility

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  • Li, Dongfang
  • Li, Xiaoxi
  • She, Mianfu
  • Sun, Hai-wei

Abstract

This paper presents a novel class of effective schemes for numerically solving Cahn–Hilliard-type equations with degenerate mobility. To overcome the difficulties from the nonlinearity and degenerate mobility, the novel schemes are developed by applying the relaxation idea and the extrapolation technique to the Runge–Kutta methods. It is shown that the novel schemes can be linearly implicit, high-order accurate, and energy-stable for the equations. Numerical experiments on the classical/fractional/nonlocal Cahn–Hilliard equations with degenerate mobility are presented to confirm the effectiveness of the schemes.

Suggested Citation

  • Li, Dongfang & Li, Xiaoxi & She, Mianfu & Sun, Hai-wei, 2026. "High-order, linearly implicit, and energy-stable methods for Cahn–Hilliard models with degenerate mobility," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 177-190.
    • Handle: RePEc:eee:matcom:v:240:y:2026:i:c:p:177-190
    DOI: 10.1016/j.matcom.2025.07.004
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