# 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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