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Article Dans Une Revue Calcolo Année : 2019

Optimality and resonances in a class of compact finite difference schemes of high order

Résumé

In this paper, we revisit the old problem of compact finite difference approximations of the homogeneous Dirichlet problem in dimension 1. We design a large and natural set of schemes of arbitrary high order, and we equip this set with an algebraic structure. We give some general criteria of convergence and we apply them to obtain two new results. On the one hand, we use Padé approximant theory to construct, for each given order of consistency, the most efficient schemes and we prove their convergence. On the other hand, we use diophantine approximation theory to prove that almost all of these schemes are convergent at the same rate as the consistency order, up to some logarithmic correction.
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Dates et versions

hal-01612326 , version 1 (06-10-2017)

Identifiants

Citer

Joackim Bernier. Optimality and resonances in a class of compact finite difference schemes of high order. Calcolo, 2019, 56 (2), pp.article 12. ⟨10.1007/s10092-019-0309-4⟩. ⟨hal-01612326⟩
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