Algorithmes d’intégration temporelle implicites couplés avec des résoluteurs d’ordre élevé
Keywords:
non-linear, instationary, implicit algorithms, homotopy, perturbation, Asymptotic Numerical Method, non-linear wavesAbstract
In this paper, we develop some new implicit algorithms for solving instationary non-linear problems. The proposed algorithms are variants of Asymptotic Numerical Methods (ANM). They are obtained by coupling the perturbation method, the homotopy technique and classical time-space discretization procedures. The efficiency of these algorithms is tested on a model for non-linear wave propagation phenomena typified by the Fisher equation. The obtained results prove a computational cost save in comparison with other algorithms for non-linear problems.
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