Symmetrized local error estimators for time-reversible one-step methods in nonlinear evolution equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:356

Article

Auzinger, Winfried¹  Hofstaetter, Harald²  Koch, Othmar² 

[1] Tech Univ Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10-E101, A-1040 Vienna, Austria

[2] Univ Wien, Inst Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

关键词: Nonlinear evolution equations;    One-step methods;    Time-reversible schemes;    Splitting methods;    Magnus integrators;    Local error estimation;   

DOI  :  10.1016/j.cam.2019.02.011

来源: Elsevier

【 摘 要 】

Prior work on computable defect-based local error estimators for (linear) time-reversible integrators is extended to nonlinear and nonautonomous evolution equations. We prove that the asymptotic results from the linear case (Auzinger and Koch, 2018) remain valid, i.e., the modified estimators yield an improved asymptotic order as the step size goes to zero. Typically, the computational effort is only slightly higher than for conventional defect-based estimators, and it may even be lower in some cases. We illustrate this by some examples and present numerical results for evolution equations of Schrodinger type, solved by either time-splitting or Magnus-type integrators. Finally, we demonstrate that adaptive time-stepping schemes can be successfully based on our local error estimators. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free