An improved local error estimator for symmetric time-stepping schemes

被引：3
|
作者：
Auzinger, Winfried [1 ]
Koch, Othmar [2 ]
机构：
[1] Vienna Univ Technol, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10-E101, A-1040 Vienna, Austria
[2] Univ Vienna, Inst Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria
来源：
APPLIED MATHEMATICS LETTERS | 2018年 / 82卷
基金：
奥地利科学基金会;
关键词：
Numerical time integration; One-step methods; Symmetric schemes; Local error estimation; SCHRODINGER-EQUATIONS; SPLITTING METHODS;
D O I：
10.1016/j.aml.2018.03.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We propose a symmetrized version of the defect to be used in the estimation of the local time-stepping error of symmetric one-step methods for the time propagation of linear autonomous evolution equations. Using the anti-commutator of the numerical flow and the right-hand side operator in the definition of the defect of the numerical approximation, a local error estimator is obtained which has higher accuracy asymptotically than an established version using the common defect. This theoretical result is illustrated for a splitting method applied to a linear Schrodinger equation. (C) 2018 Elsevier Ltd. All rights reserved.
引用
收藏
页码：106 / 110
页数：5
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