Numerical Algorithms

, Volume 33, Issue 1–4, pp 421–431 | Cite as

Approximation and Prediction of the Numerical Solution of Some Burgers Problems

  • Marc Prévost
  • Denis Vekemans
Article

Abstract

The Aitken's Δ2-prediction of Brezinski has already been used by Morandi Cecchi et al. in order to compute a numerical approximation of the solution of a parabolic initial-boundary value problem. This method consists in two consecutive steps: the first one is the approximation with a finite elements method, where the solution of the involved nonlinear system is computed by Gauss–Seidel method; the second one is a prediction of further terms with Aitken's Δ2-process. By comparison with this method, we use other methods of prediction in another way. First, we consider a generalization of Δ2-prediction, the so-called ε-prediction. In this paper, we only use vector prediction which is more stable than the scalar one. Then, the methods of prediction presented can be used in order to predict the starting vector of the Gauss–Seidel method.

approximation prediction ε-prediction vector prediction Burgers problem 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Marc Prévost
    • 1
  • Denis Vekemans
    • 1
  1. 1.Laboratoire de Mathématiques Pures et AppliquéesUniversité du Littoral Côte d'Opale, Centre Universitaire de la Mi-VoixCalais CédexFrance

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