Defect-based local error estimators for splitting methods, with application to Schrodinger equations, Part I: The linear case

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Auzinger, Winfried¹  Koch, Othmar¹  Thalhammer, Mechthild^2,3 

[1] Vienna Univ Technol, Inst Anal & Sci Comp, A-1040 Vienna, Austria

[2] Leopold Franzens Univ Innsbruck, Inst Math, A-6020 Innsbruck, Austria

[3] Univ Bundeswehr Munchen, Fak Luft & Raumfahrttech, Inst Math & Rechneranwendung, D-85577 Neubiberg, Germany

关键词: Linear evolution equations;    Time-dependent linear Schrodinger equations;    Exponential operator splitting methods;    Defect correction;    A priori local error estimates;    A posteriori local error estimates;   

DOI  :  10.1016/j.cam.2012.01.001

来源: Elsevier

【 摘 要 】

We introduce a defect correction principle for exponential operator splitting methods applied to time-dependent linear Schrodinger equations and construct a posteriori local error estimators for the Lie-Trotter and Strang splitting methods. Under natural commutator bounds on the involved operators we prove asymptotical correctness of the local error estimators, and along the way recover the known a priori convergence bounds. Numerical examples illustrate the theoretical local and global error estimates. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free