Fourth order accurate numerical solution of the sine-Gordon equation: using the summation-by-parts simultaneous approximation term method
Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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.
TVE, 13 040 juni
IdentifiersURN: urn:nbn:se:uu:diva-202553OAI: oai:DiVA.org:uu-202553DiVA: diva2:632361
Master Programme in Engineering Physics