线性反应扩散方程的时间变步长BDF2格式的最优误差估计OACSTPCD
SHARP ERROR ESTIMATE OF BDF2 SCHEME WITH VARIABLE TIME STEPS FOR LINEAR REACTION-DIFFUSION EQUATIONS
虽然时间变步长的两步向后差分公式(BDF2)在模拟多尺度动力学具有重要的价值和广泛的应用,但其稳定性和收敛性分析仍不完整.在本工作中,我们重新讨论了线性反应扩散问题的BDF2格式.利用[11]中离散正交卷积(DOC)核的技巧,引入离散互补卷积(DCC)核的概念,我们证明了在相邻时间步长比条件0＜rk:=τk/τk-1≤rmax ≈ 4.8645下,BDF2格式是无条件稳定的且具有二阶收敛率.我们的分析表明,二阶收敛性是最优且鲁棒的.鲁棒性指对于任…查看全部>>
While the variable time-steps two-step backward differentiation formula(BDF2)is valuable and widely used to capture the multi-scale dynamics of model solutions,the stability and convergence of BDF2 with variable time steps still remain incomplete.In this work,we re-visit BDF2 scheme for linear diffusion-reaction problem.By using the technique of the discrete orthogonal convolution(DOC)kernels developed in[11],and introducing the concept of the dis-crete comp…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
BDF2DOCDCC时间变步长最优误差估计
BDF2DOCDCCvariable time stepssharp error estimate
《数学杂志》 2021 (6)
471-488,18
Supported by NSFC under grant Nos.11771035 and NSAF U1930402,the Natural Science Foundation of Hubei Province No.2019CFA007.The numerical simulations in this work have been done on the supercomputing system in the Supercomputing Center of Wuhan University.
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