IMEX methods for thin-film equations and Cahn-Hilliard equations with variable mobility
<|reference_start|>IMEX methods for thin-film equations and Cahn-Hilliard equations with variable mobility: We explore a class of splitting schemes employing implicit-explicit (IMEX) time-stepping to achieve accurate and energy-stable solutions for thin-film equations and Cahn-Hilliard models with variable mobility. This splitting method incorporates a linear, constant coefficient implicit step, facilitating efficient computational implementation. We investigate the influence of stabilizing splitting parameters on the numerical solution computationally, considering various initial conditions. Furthermore, we generate energy-stability plots for the proposed methods, examining different choices of splitting parameter values and timestep sizes. These methods enhance the accuracy of the original bi-harmonic-modified (BHM) approach, while preserving its energy-decreasing property and achieving second-order accuracy. We present numerical experiments to illustrate the performance of the proposed methods.<|reference_end|>
@article{orizaga2024imex,
    title={IMEX methods for thin-film equations and Cahn-Hilliard equations with
  variable mobility},
    author={Saulo Orizaga and Thomas Witelski},
    journal={Computational Materials Science -2024 - in production},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.19483},
    primaryClass={math.NA cs.NA math-ph math.MP}
}