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Splines and Ocean Wave Modelling

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Numerical Methods and Software Tools in Industrial Mathematics

Abstract

The chapter introduces spline functions as approximants in the approximate solution of differential equations. These solutions are continuous and accurate such that results can be evaluated anywhere within the solution domain. The details of this method for solving differential equations are worked out for an example of great practical importance: The fully nonlinear equations of water waves.

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Bibliography

  1. C. de Boor, A Practical Guide to Splines, Applied Mathematical Sciences 27. Springer-Verlag, 1978.

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  2. E. Mehlum, Curve and surface fitting based on variational criteriae for smoothness, PhD. thesis, University of Oslo, Norway and SINTEF report, 1969.

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  3. X. Cai and E. Mehlum, Two fragments of a method for fully nonlinear simulations of water waves, Waves and Nonlinear Processes in Hydrodynamics, J. Grue et al.(eds.) pp.37–50. Kluwer Academic Publ. 1996

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  4. W. P. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in C, 2nd Edition. Cambridge University Press, 1992.

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  5. V. E. Zakharov, Stability of periodic waves of finite amplitude on the surface of a deep fluid, J. Appl. Mech. Tech. Phys., 9. pp. 190–194. (English tansl.), 1968

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Author information

Authors and Affiliations

  1. SINTEF, P.O. Box 124, Blindern, Oslo, 0314, Norway

    Even Mehlum

Authors
  1. Even Mehlum
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Editor information

Editors and Affiliations

  1. SINTEF Applied Mathematics, Blindern, Oslo, N-0314, Norway

    Morten Dæhlen

  2. Department of Informatics, University of Oslo, N-0316, Oslo, Norway

    Aslak Tveito

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© 1997 Springer Science+Business Media New York

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Mehlum, E. (1997). Splines and Ocean Wave Modelling. In: Dæhlen, M., Tveito, A. (eds) Numerical Methods and Software Tools in Industrial Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1984-2_11

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  • DOI: https://doi.org/10.1007/978-1-4612-1984-2_11

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7367-7

  • Online ISBN: 978-1-4612-1984-2

  • eBook Packages: Springer Book Archive

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