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  A three operator split-step method covering a larger set of non-linear partial differential equations

Zia, H. (2017). A three operator split-step method covering a larger set of non-linear partial differential equations. Communications in Nonlinear Science and Numerical Simulation, 47, 277-291. doi:10.1016/j.cnsns.2016.11.020.

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 Urheber:
Zia, Haider1, Autor           
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1Miller Group, Atomically Resolved Dynamics Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_1938288              

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Schlagwörter: Mathematics; Numerical Analysis; Mathematical Physics
 Zusammenfassung: This paper describes an updated Fourier based split-step method that can be applied to a greater class of partial differential equations, than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized non-linear Schr\"odinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

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Sprache(n): eng - English
 Datum: 2016-11-222016-06-132016-11-232016-11-292017-06
 Publikationsstatus: Erschienen
 Seiten: 15
 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: Expertenbegutachtung
 Identifikatoren: arXiv: 1604.01138
DOI: 10.1016/j.cnsns.2016.11.020
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Titel: Communications in Nonlinear Science and Numerical Simulation
Genre der Quelle: Zeitschrift
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Ort, Verlag, Ausgabe: Amsterdam, Netherlands : Elsevier B.V.
Seiten: - Band / Heft: 47 Artikelnummer: - Start- / Endseite: 277 - 291 Identifikator: ISSN: 1007-5704
CoNE: https://pure.mpg.de/cone/journals/resource/1007-5704