2025/12/01 by Wenbin Chen, Chen, Wenbin, Zhaohui Fu +5
Engineering · Materials Science · #65M12 #65M70 #65Z05 #Advanced Numerical Methods in Computational Mathematics #Convergence (economics) #Exponential function #Extension (predicate logic) #FOS: Mathematics #Fluid Dynamics and Thin Films #Lipschitz continuity #Monotonic function #Nonlinear system #Numerical Analysis (math.NA) #Perturbation (astronomy) #Scheme (mathematics) #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.2512.01601
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/12/01 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28
We analyze a variable-step extension of a family of arbitrarily high-order exponential time differencing multistep (ETD-MS) schemes recently developed by the authors. We prove that the schemes are unconditionally stable in the sense that a modified energy-representing a slight perturbation of the original energy-decreases monotonically over time, provided the nonlinearity is Lipschitz continuous in some appropriate sense. Moreover, we establish optimal-order convergence under mild conditions on the time-step size and local time-step ratio. Numerical experiments on the thin film epitaxial growth model without slope selection, employing a novel variable-step second-order scheme, validate the theoretical findings as well as its potential in developing highly efficient time-adaptive solution.