数学杂志2022，Vol.42Issue(5)：377-401,25.
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
SHARP ERROR ESTIMATE OF BDF2 SCHEME WITH VARIABLE TIME STEPS FOR MOLECULAR BEAM EPITAXIAL MODELS WITHOUT SLOP SELECTION
摘要
Abstract
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 developed techniques of the discrete orthogonal convolution(DOC)and dis-crete complementary convolution(DCC)kernels,and present the robust and sharp second-order convergence of the BDF2 scheme with the new ratio condition:rk≤4.8645-δ.The robustness means the convergence does not need other constrained condition on the time steps except for rk≤4.8645-δ.In addition,our analysis shows that the first-order BDF1 scheme for the start step is enough to ensure the globally optimal convergence order.This is,the choice of BDF1 scheme for the start step does not bring the loss of global second-order convergence.Numerical examples are provided to demonstrate the theoretical analysis.关键词
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Key words
BDF2 with variable time steps/the discrete orthogonal convolution(DOC)ker-nels/the discrete complementary convolution(DCC)kernels/the error convolution structure(ECS)/sharp error estimate/MBE models分类
数理科学引用本文复制引用
张继伟,赵成超..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[J].数学杂志,2022,42(5):377-401,25.基金项目
Supported by NSFC(12171376,2020-JCJQ-ZD-029) （12171376,2020-JCJQ-ZD-029）
Natural Science Foun-dation of Hubei Province(2019CFA007) （2019CFA007）
the Fundamental Research Funds for the Central Universities(2042021kf0050). （2042021kf0050）
