Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2017;57(1):55-74.
doi: 10.1007/s10543-016-0626-9. Epub 2016 Jul 28.

Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes

Winfried Auzinger  1 , Harald Hofstätter  1 , David Ketcheson  2 , Othmar Koch  3
Affiliations

Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes

Winfried Auzinger et al. BIT Numer Math. 2017.

Abstract

We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.

Keywords: Embedded methods; Evolution equations; Free Lie algebra; Local error; Order conditions; Splitting methods.

PubMed Disclaimer

References

    1. Auzinger W, Herfort W. Local error structures and order conditions in terms of Lie elements for exponential splitting schemes. Opusc. Math. 2014;34:243–255. doi: 10.7494/OpMath.2014.34.2.243. - DOI
    1. Auzinger W, Hofstätter H, Koch O, Thalhammer M. Defect-based local error estimators for splitting methods, with application to Schrödinger equations. Part III: the nonlinear case. J. Comput. Appl. Math. 2014;273:182–204. doi: 10.1016/j.cam.2014.06.012. - DOI
    1. Auzinger, W., Koch. O.: Coefficients of various splitting methods. http://www.asc.tuwien.ac.at/~winfried/splitting/
    1. Auzinger W, Koch O, Thalhammer M. Defect-based local error estimators for splitting methods, with application to Schrödinger equations. Part I: the linear case. J. Comput. Appl. Math. 2012;236:2643–2659. doi: 10.1016/j.cam.2012.01.001. - DOI
    1. Auzinger W, Koch O, Thalhammer M. Defect-based local error estimators for splitting methods, with application to Schrödinger equations. Part II: higher-order methods for linear problems. J. Comput. Appl. Math. 2013;255:384–403. doi: 10.1016/j.cam.2013.04.043. - DOI

LinkOut - more resources