Dual Schur Method in Time for Nonlinear ODE

Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)

Abstract

We developed parallel time domain decomposition methods to solve systems of linear ordinary differential equations (ODEs) based on the Aitken-Schwarz [5] or primal Schur complement domain decomposition methods [4]. The methods require the transformation of the initial value problem in time defined on ]0, T] into a time boundary values problem. Let f(t, y(t)) be a function belonging to \(\mathcal{C}^{1}(\mathbb{R}^{+}, \mathbb{R}^{d})\) and consider the Cauchy problem for the first order ODE:
$$\displaystyle{ \left \{\begin{array}{@{}l@{\quad }l@{}} \dot{y} = f(t,y(t)),\,t \in ]0,T],\;y(0) =\alpha \in \mathbb{R}^{d}.\quad \end{array} \right. }$$
(1)

Notes

Acknowledgements

This work was supported by the French National Agency of Research through the project ANR MONU-12-0012 H2MNO4. This work was granted access to the HPC resources of CINES under the allocation 2014-c2014066099 made by GENCI (Grand Equipement National de Calcul Intensif) and used the HPC resources of Center for the Development of Parallel Scientific Computing (CDCSP) of University Lyon 1.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Biostatistics and Computational BiologyUniversity of RochesterRochester, NYUSA
  2. 2.University of LyonUniversity Lyon 1, CNRSLyonFrance

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