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Numerical Methods for the Benjamin-Ono Equation
Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, Department of Mathematical Sciences.
2013 (English)MasteroppgaveStudent thesis
Abstract [en]

In this thesis, we compare four numerical methods for solving the Benjamin-Ono equation. The numerical methods are presented in detail, and we compare them for different test problems. We derive the Hirota bilinear form of the Benjamin-Ono equation, and present spatially periodic exact solutions. The best numerical method is Chan and Kerkhoven's Semi-Implicit Fourier pseudospectral method, originally intended for the Korteweg-de Vries equation. In the last chapter, we study the zero dispersion limit for the Korteweg-de Vries and Benjamin-Ono equation. We observe that the small dispersion term forces the shock formation in the solution to become travelling waves.

Place, publisher, year, edition, pages
Institutt for matematiske fag , 2013. , 79 p.
URN: urn:nbn:no:ntnu:diva-20738Local ID: ntnudaim:8553OAI: diva2:617038
Available from: 2013-04-21 Created: 2013-04-21 Last updated: 2013-06-22Bibliographically approved

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