Numerische Mathematik

, Volume 134, Issue 2, pp 249–274 | Cite as

Convergence of finite difference schemes for the Benjamin–Ono equation

  • Rajib Dutta
  • Helge Holden
  • Ujjwal Koley
  • Nils Henrik Risebro
Article

Abstract

In this paper, we analyze finite difference schemes for Benjamin–Ono equation, \(u_t= u u_x + H u_{xx}\), where H denotes the Hilbert transform. Both the decaying case on the full line and the periodic case are considered. If the initial data are sufficiently regular, fully discrete finite difference schemes shown to converge to a classical solution. Finally, the convergence is illustrated by several examples.

Mathematics Subject Classification

Primary 35Q53 65M06 Secondary 35Q51 65M12 65M15 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Rajib Dutta
    • 1
  • Helge Holden
    • 1
    • 2
  • Ujjwal Koley
    • 3
  • Nils Henrik Risebro
    • 1
  1. 1.Department of MathematicsUniversity of OsloOsloNorway
  2. 2.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway
  3. 3.Tata Institute of Fundamental Research Centre, Centre For Applicable MathematicsBangaloreIndia

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