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.

翻译：本文研究一类采用隐显式时间步进的分裂格式，用于求解变迁移率薄膜方程和Cahn-Hilliard模型的精确且能量稳定的解。该分裂方法包含具有线性常系数隐式步骤，有利于高效计算实现。我们通过数值计算研究了稳定化分裂参数对数值解的影响，并考虑了多种初始条件。此外，我们为所提方法绘制了能量稳定性曲线，考察了不同分裂参数值和时间步长的选择。这些方法在保持原双调和修正方法能量递减特性和二阶精度的同时，提升了其计算精度。我们通过数值实验展示了所提方法的性能。