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Fourth order accurate numerical solution of the sine-Gordon equation: using the summation-by-parts simultaneous approximation term method
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.
2013 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

This project deals with creating a numerical solver of the sine-Gordon equation using the summation- by- parts and simultaneous approximation term method in combination with a finite difference time- stepping method as well as a Runge-Kutta time-stepping method. All implementations were done with fourth order accuracy and the theoretical work involved in deriving such a finite difference time-stepping method for the sine-Gordon equation is presented.

Both the finite difference and the Runge-Kutta time- stepping methods conserved the energy of the solutions. The only significant difference between the two time-stepping methods was that the finite difference method executed significantly faster than the Runge-Kutta method. However, the Runge- Kutta method is easier to implement and may therefore be preferable when execution time is non-vital. 

Place, publisher, year, edition, pages
2013. , 27 p.
Series
TVE, 13 040 juni
Keyword [en]
sine-Gordon
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-202553OAI: oai:DiVA.org:uu-202553DiVA: diva2:632361
Educational program
Master Programme in Engineering Physics
Supervisors
Examiners
Available from: 2013-06-26 Created: 2013-06-24 Last updated: 2013-06-26Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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Language
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  • nn-NB
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Output format
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