The decomposition method and linear partial differential equations

  • Authors:

  • Lionel Gabet

  • Affiliations:

  • Université PARIS 6, Laboratoire MEDIMAT 15 rue de l'Ecole de Médecine, 75270 Paris Cedex 06, France and Ecole Centrale de Paris, Laboratoire MAS Grande Voie des Vignes, 92295 Châten ...

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 1993

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Abstract

After a summary of the general principles on which the decomposition works on and after a review of the difficulties raised by PDE, the implementation of the method is explained with a simple case. Afterwards, it is proved that this method can be used to solve hyperbolic, elliptic and parabolic equations either with initial or boundary conditions. For the first time, a concrete example illustrates with numerical results how the method is powerful when complex calculations are really carried out. General remarks and advice conclude this study.