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Volume 4, Issue 1
Multi-Product Expansion with Suzuki's Method: Generalization

Jürgen Geiser

DOI: 10.4208/nmtma.2011.m9010

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 68-91.

Published online: 2011-04

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  • Abstract

In this paper we discuss the extension to exponential splitting methods with respect to time-dependent operators. We concentrate on the Suzuki's method, which incorporates ideas into the time-ordered exponential of [3, 11, 12, 34]. We formulate the methods with respect to higher order by using kernels for an extrapolation scheme. The advantages include more accurate and less computational intensive schemes for special time-dependent harmonic oscillator problems. The benefits of the higher order kernels are given on different numerical examples.

  • Keywords

Suzuki's method, multiproduct expansion, multiplicate and additive splitting schemes, exponential splitting.

  • AMS Subject Headings

65M15, 65L05, 65M71

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-4-68, author = {Jürgen Geiser}, title = {Multi-Product Expansion with Suzuki's Method: Generalization}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {1}, pages = {68--91}, abstract = {

In this paper we discuss the extension to exponential splitting methods with respect to time-dependent operators. We concentrate on the Suzuki's method, which incorporates ideas into the time-ordered exponential of [3, 11, 12, 34]. We formulate the methods with respect to higher order by using kernels for an extrapolation scheme. The advantages include more accurate and less computational intensive schemes for special time-dependent harmonic oscillator problems. The benefits of the higher order kernels are given on different numerical examples.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.m9010}, url = {http://global-sci.org/intro/article_detail/nmtma/5959.html} }
TY - JOUR T1 - Multi-Product Expansion with Suzuki's Method: Generalization AU - Jürgen Geiser JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 68 EP - 91 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.m9010 UR - https://global-sci.org/intro/article_detail/nmtma/5959.html KW - Suzuki's method, multiproduct expansion, multiplicate and additive splitting schemes, exponential splitting. AB -

In this paper we discuss the extension to exponential splitting methods with respect to time-dependent operators. We concentrate on the Suzuki's method, which incorporates ideas into the time-ordered exponential of [3, 11, 12, 34]. We formulate the methods with respect to higher order by using kernels for an extrapolation scheme. The advantages include more accurate and less computational intensive schemes for special time-dependent harmonic oscillator problems. The benefits of the higher order kernels are given on different numerical examples.

Jürgen Geiser. (2011). Multi-Product Expansion with Suzuki's Method: Generalization. Numerical Mathematics: Theory, Methods and Applications. 4 (1). 68-91. doi:10.4208/nmtma.2011.m9010
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