Titre : |
Efficient solution of a wave equation with fractional order dissipative terms |
Année : |
2010 |
Type : |
article (revue avec comité de lecture) |
Auteurs : |
H. Haddar, J.-R. Li, D. Matignon |
Résumé : |
We consider a wave equation with fractional order dissipative terms modeling viscothermal
losses on the lateral walls of a duct. Diffusive realizations of fractional
derivatives are used, first to prove existence and uniqueness results, then to design
a numerical scheme which avoids the storage of the entire history of past data. Two
schemes are proposed depending on the choice of a quadrature rule in the Laplace
domain. The first one mimics the continuous energy balance but suffers from a loss
of accuracy in long time simulation. The second one provides uniform control of the
accuracy. However, even though the latter is more efficient and numerically stable
under the standard CFL condition, no discrete energy balance has been yet found
for it. Numerical results of comparisons with a closed-form solutions are provided |
Thèmes : |
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Référence : |
Journal of Computational and Applied Mathematics - vol. 234(6) (pp 2003-2010 ) |