Wavelets pp 269-283 | Cite as

Towards a Method for Solving Partial Differential Equations Using Wavelet Bases

  • V. Perrier
Part of the Inverse Problems and Theoretical Imaging book series (IPTI)


Wavelets present good properties of global approximation (good frequency localization) and their spatial localization allows precise approximation of discontinuities, without producing spurious fluctuations all over the domain.


Galerkin Method Collocation Method Collocation Point Wavelet Base Gibbs Phenomenon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Loisel, P., “Resolution des equations de Navier-Stokes compressibles instationnaires par méthode spectrale de Tchebychefi Thése Université Paris VI (1986)Google Scholar
  2. [2]
    Loisel, P., Pernaud-Thomas, B., “Méthodes numériques d’ordre élevé appliquées au calcul d’écoulements compressibles Thèse Université Paris VI, to be published (April 1988).Google Scholar
  3. [3]
    Grossmann, A., Morlet, J., “Decomposition of Hardy functions into square integrable wavelets of constant shape SIAM J. Math. Anal. 15, 723–736 (1884).MathSciNetGoogle Scholar
  4. [4]
    Meyer, Y., “Principe d’incertitude, bases hilbertiennes et algèbres d’operateurs Séminaire Bourbaki, nr. 662 (Feb. 1986).Google Scholar
  5. [5]
    Daubechies, L, “Orthonormal bases of supported wavelets Bell. lab. (1987).Google Scholar
  6. [6]
    Battle, G., “A block spin construction of ondelettes, Part. 1: Lemarié functions Comm. Math. Phys. (1987).Google Scholar
  7. [7]
    Lemarié, P.G., “Ondelettes à localisation exponentielle “Journ. de Math. Pures et Appl., to be published.Google Scholar
  8. [8]
    Goupillaud, P., Grossmann, A. and Morlet, J., “Cyclo-octave and related transforms in seismic signal analysis Geoexploration 23, 85–102 (1984).Google Scholar
  9. [9]
    Mallat, S., “A theory for multiresolution signal decomposition preprint GRASP Lab, Dept., of computer and Information Science, Univ. of Pennsylvania (May 1987).Google Scholar
  10. [10]
    Kronland-Martinet, R., Morlet, J. and Grossmann A., “Analysis of sound patterns through wavelet transforms International Journal on Pattern Analysis and Artificiel Intelligence, vol.1 (Jan. 1987).Google Scholar
  11. [11]
    Meyer, Y., “Wavelets and operators Ceremade, Cours de l’Université Paris Dauphine (1987).Google Scholar
  12. [12]
    Meyer, Y., “Ondelettes, fonctions splines et analyses graduées “, Univ. of Torino (1986).Google Scholar
  13. [13]
    Grossmann, A., Holschneider, M., Kronland-Martinet, R. and Morlet, J., Detection of abrupt changes in sound signals with the help of wavelet transforms “, preprint, Centre de Physique Theorique, CNRS, Marseille, (1987).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • V. Perrier
    • 1
  1. 1.ONERAChâtillon CedexFrance

Personalised recommendations