2014
DOI: 10.1051/proc/201445033
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Borel-Laplace summation method used as time integration scheme

Abstract: Abstract.A time integration method for the resolution of ordinary and partial differential equations is proposed. The method consists in computing a formal solution as a (eventually divergent) time series. Next, the Borel resummation method is applied to deduce an (sectorial) analytical solution. The speed and spectral properties of the scheme are analyzed through some examples. Applications to fluid mechanics are presented.Résumé. On propose une méthode numérique d'intégration temporelle d'équations différent… Show more

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Cited by 9 publications
(9 citation statements)
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“…For example, it generally allows much larger time steps than other explicit methods for the resolution of many problems [28]. Its ability to cross some types of singularities, its high-order symplecticity, or its high-order iso-spectrality in solving a Lax pair problem have been stated in [29]. Another advantage of BL is that decreasing or increasing the approximation order is as simple as changing the value of a parameter in the code.…”
Section: Introductionmentioning
confidence: 99%
“…For example, it generally allows much larger time steps than other explicit methods for the resolution of many problems [28]. Its ability to cross some types of singularities, its high-order symplecticity, or its high-order iso-spectrality in solving a Lax pair problem have been stated in [29]. Another advantage of BL is that decreasing or increasing the approximation order is as simple as changing the value of a parameter in the code.…”
Section: Introductionmentioning
confidence: 99%
“…The theory of Borel summation can be found, for example, in [2,[19][20][21]. Some other works on BPL, as a time integrator, can be found in [7,22]. In this section, we present very briefly the Borel-Padé-Laplace algorithm, integrated into a numerical scheme.…”
Section: Borel-laplace Integratormentioning
confidence: 99%
“…For example, it generally allows much bigger time steps than other explicit methods for the resolution of many problems [21]. Its ability to cross some types of singularities, its high-order symplecticity, or its high-order iso-spectrality in solving a Lax pair problem have been stated in [22]. Another advantage of BL is that lowering or raising the approximation order is as simple as changing the value of a parameter in the code.…”
Section: Introductionmentioning
confidence: 99%