无倾斜选择的分子束外延模型变步长BDF2格式的最优误差估计OACSTPCD
SHARP ERROR ESTIMATE OF BDF2 SCHEME WITH VARIABLE TIME STEPS FOR MOLECULAR BEAM EPITAXIAL MODELS WITHOUT SLOP SELECTION
对于没有斜率选择的分子束外延模型,具有可变时间步长的两步向后微分公式(BDF2)的稳定性和收敛性仍未被完全解决.在本文中,我们首先证明了该BDF2格式在新的相邻时间步长比条件下保持修正的能量耗散定律:rk:=τk/τk-1≤4.8645-δ,其中δ＞0是给定的任意小常数.然后,我们介绍了最近发展的离散正交卷积(DOC)和离散互补卷积(DCC)核技巧,并在新的比率条件rk≤4.8645-6下给出了 BDF2格式的鲁棒且最优的二阶收敛性.鲁棒性意味着…查看全部>>
The stability and convergence of two-step backward differentiation formula(BDF2)with variable time steps still remain incomplete for solving the molecular beam epi-taxial model without slope selection.In this paper,we first prove the proposed BDF2 scheme to preserve a modified energy dissipation law under a new adjacent time-step ratio condition:rk:=Tk/Tk-1≤4.8645-δ,where δ＞0 is a given arbitrarily small constant.After that,we introduce the recently develope…查看全部>>
张继伟;赵成超
武汉大学数学与统计学院计算科学湖北省重点实验室,湖北武汉430072
数理科学
变步长BDF2离散正交卷积(DOC)核离散互补卷积(DCC)核误差卷积结构(ECS)最优误差估计分子束外延(MBE)模型
BDF2 with variable time stepsthe discrete orthogonal convolution(DOC)ker-nelsthe discrete complementary convolution(DCC)kernelsthe error convolution structure(ECS)sharp error estimateMBE models
《数学杂志》 2022 (5)
非局部模型的基础理论和数值方法研究
377-401,25
Supported by NSFC(12171376,2020-JCJQ-ZD-029)Natural Science Foun-dation of Hubei Province(2019CFA007)the Fundamental Research Funds for the Central Universities(2042021kf0050).
评论