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Preprints, Working Papers, ... Year : 2022

Approximation and prediction of the numerical solution of some Burgers problems

Abstract

The Aitken's ∆ 2-prediction of Brezinski has already been used by Morandi Cecchi, Redivo Zaglia and Scenna in order to approximate the solution of a parabolic initial-boundary value problem. The method used consists in two consecutive steps : the approximation with a finite elements method where the solution of system of nonlinear equations is computed by Gauss-Seidel method, followed by a prediction with Aitken's ∆ 2-process. By comparison with this method, we use other methods of prediction and in another way. On the first hand, we not only use the ∆ 2-prediction and we can consider a generalization of this method of prediction, the ε-prediction. Moreover, in this paper, we only make use of vector prediction which is more stable than the scalar one. On the other hand, the methods of prediction presented will be used in order to predict the starting vector of the Gauss-Seidel method.
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Dates and versions

hal-03663548 , version 1 (10-05-2022)

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  • HAL Id : hal-03663548 , version 1

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Marc Prévost, Denis Vekemans. Approximation and prediction of the numerical solution of some Burgers problems. 2022. ⟨hal-03663548⟩
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