Error estimates for a class of energy dissipative IMEX Runge–Kutta schemes applied to the no-slope-selection thin film model

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-12 DOI:10.1016/j.cnsns.2025.108797

Xueqing Teng , Xiaowei Chen , Hong Zhang

{"title":"Error estimates for a class of energy dissipative IMEX Runge–Kutta schemes applied to the no-slope-selection thin film model","authors":"Xueqing Teng , Xiaowei Chen , Hong Zhang","doi":"10.1016/j.cnsns.2025.108797","DOIUrl":null,"url":null,"abstract":"<div><div>In this work, we rigorously establish the convergence analysis and error estimates for a class of up to third-order implicit-explicit Runge–Kutta (IMEX RK) schemes for the no-slope-selection (NSS) thin film growth model, which follows from detailed eigenvalue bound estimates for constructed operators and nonlinear analysis of the NSS equation. To our knowledge, this convergence analysis is the first such result of applying a third-order accurate IMEX RK scheme to the epitaxial growth model. Additionally, by introducing a linear stabilization term to the system and employing the Fourier pseudo-spectral method for spatial discretization, we reestablish the energy stability of the first- to third-order IMEX RK schemes in a concise way. Numerical experiments are performed to verify the accuracy of the scheme, and to illustrate some theoretical results such as mass conservation, energy decay rate, and growth rates of surface roughness and mound width.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"147 ","pages":"Article 108797"},"PeriodicalIF":3.4000,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570425002084","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

In this work, we rigorously establish the convergence analysis and error estimates for a class of up to third-order implicit-explicit Runge–Kutta (IMEX RK) schemes for the no-slope-selection (NSS) thin film growth model, which follows from detailed eigenvalue bound estimates for constructed operators and nonlinear analysis of the NSS equation. To our knowledge, this convergence analysis is the first such result of applying a third-order accurate IMEX RK scheme to the epitaxial growth model. Additionally, by introducing a linear stabilization term to the system and employing the Fourier pseudo-spectral method for spatial discretization, we reestablish the energy stability of the first- to third-order IMEX RK schemes in a concise way. Numerical experiments are performed to verify the accuracy of the scheme, and to illustrate some theoretical results such as mass conservation, energy decay rate, and growth rates of surface roughness and mound width.

查看原文本刊更多论文

应用于无坡度选择薄膜模型的一类能量耗散IMEX龙格-库塔格式的误差估计

在这项工作中，我们严格地建立了一类高达三阶隐式-显式龙格-库塔（IMEX RK）格式的无斜率选择（NSS）薄膜生长模型的收敛分析和误差估计，这是由构造算子的详细特征值界估计和NSS方程的非线性分析得出的。据我们所知，这种收敛分析是将三阶精确IMEX RK方案应用于外延生长模型的第一个这样的结果。此外，通过在系统中引入线性稳定项并采用傅里叶伪谱方法进行空间离散化，我们以简洁的方式重建了一阶至三阶IMEX RK格式的能量稳定性。数值实验验证了该方案的准确性，并举例说明了质量守恒、能量衰减率、表面粗糙度和土墩宽度的增长率等理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.