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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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 Creators:
Zia, Haider1, Author              
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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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Free keywords: Mathematics; Numerical Analysis; Mathematical Physics
 Abstract: 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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Language(s): eng - English
 Dates: 2016-11-222016-06-132016-11-232016-11-292017-06
 Publication Status: Published in print
 Pages: 15
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1604.01138
DOI: 10.1016/j.cnsns.2016.11.020
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Title: Communications in Nonlinear Science and Numerical Simulation
Source Genre: Journal
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Publ. Info: Amsterdam, Netherlands : Elsevier B.V.
Pages: - Volume / Issue: 47 Sequence Number: - Start / End Page: 277 - 291 Identifier: ISSN: 1007-5704
CoNE: https://pure.mpg.de/cone/journals/resource/1007-5704