Bibliography

Major publications by the team in recent years

[1]

G. Andreoiu, E. Faou.
Complete asymptotics for shallow shells, in: Asymptotic analysis, 2001, vol. 25, p. 239-270.

[2]

A. Aubry, P. Chartier.
On improving the convergence of Radau IIA methods when applied to index-2 DAEs, in: SIAM Journal on Numerical Analysis, 1998, vol. 35, n^o 4, p. 1347-1367.

[3]

A. Aubry, P. Chartier.
Pseudo-symplectic Runge-Kutta methods, in: BIT, 1998, vol. 38, p. 439–461.

[4]

F. Castella.
From the von Neumann equation to the Quantum Boltzmann equation in a deterministic framework, in: J. Stat. Phys., 2001, vol. 104–1/2, p. 387–447.

[5]

F. Castella.
Propagation of space moments in the Vlasov-Poisson Equation and further results, in: Ann. I.H.P., Anal. NonLin., 1999, vol. 16–4, p. 503–533.

[6]

R. Chan, P. Chartier, A. Murua.
Post-projected Runge-Kutta methods for index-2 differential-algebraic equations, in: Applied Numerical Mathematics, 2002, vol. 42, n^o 1-3, p. 77-94.

[7]

M. Dauge, I. Djurdjevic, E. Faou, A. Roessle.
Eigenmode asymptotics in thin elastic plates, in: J. Math. Pures Appl., 1999, vol. 78, p. 925-954.

[8]

E. Faou.
Elasticity on a thin shell: Formal series solution, in: Asymptotic analysis, 2002, vol. 31, p. 317-361.

Publications of the year

Articles in International Peer-Reviewed Journal

[9]

N. B. Abdallah, F. Castella, F. Fendt, F. Méhats.
The strongly confined Schrödinger-Poisson system for the transport of electrons in a nanowire, in: SIAM Journal on Applied Mathematics, 2009, vol. 69, n^o 4, p. 1162–1173.

[10]

F. Castella, P. Chartier, S. Descombes, G. Vilmart.
Splitting methods with complex times for parabolic equations, in: BIT Numerical Mathematics, 2009, vol. 49.

[11]

F. Castella, P. Chartier, E. Faou.
An averaging technique for highly-oscillatory Hamiltonian problems, in: SIAM J. Numer. Anal., 2009, vol. 47, p. 2808-2837.

[12]

F. Castella, G. Dujardin.
Propagation of Gevrey regularity over long times for the fully discrete Lie Trotter splitting scheme applied to the linear Schrödinger equation, in: Math. Mod. An. Num., 2009, vol. 43, n^o 4, p. 651–676.

[13]

F. Castella, G. Dujardin, B. Sericola.
Moments analysis in Markov reward models, in: Methodology and Computing in Applied Probability, 2009.

[14]

P. Chartier, E. Darrigrand, E. Faou.
A Fast Multipole Method for Geometric Numerical Integrations of Hamiltonian Systems, in: BIT Numerical Analysis, 2009, Under minor revision for BIT Numerical Analysis.

[15]

P. Chartier, E. Hairer, G. Vilmart.
Algebraic structures of B-series, in: Foundations of Computational Mathematics, 2009, Under minor revision for FOCM.

[16]

P. Chartier, A. Murua.
An algebraic theory of order, in: M2AN Math. Model. Numer. Anal., 2009, vol. 43.

[17]

P. Chartier, J.-M. Sanz-Serna, A. Murua.
Higher-order averaging, formal series and numerical integration I: B-series, in: Foundations of Computational Mathematics, 2009, submitted.

[18]

A. Crudu, A. Debussche, O. Radulescu.
Hybrid stochastic simplifications for multiscale gene networks, in: BMC Systems Biology, 2009, vol. 89, n^o 3.

[19]

A. de Bouard, A. Debussche.
Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise, in: Elec. Journal Proba., 2009, vol. 31, n^o 58.

[20]

A. Debussche.
Weak approximation of stochastic partial differential equations: the nonlinear case, in: Math. Comp., 2009, to appear.

[21]

A. Debussche, E. Faou.
Modified energy for split-step methods applied to the linear Schrödinger equation., in: SIAM J. Numer. Anal., 2009, vol. 47, p. 3705–3719.

[22]

A. Debussche, J. Printems.
Weak order for the discretization of the stochastic heat equation, in: Math. Comp., 2009, vol. 266, n^o 78, p. 845-863.

[23]

A. Debussche, J. Vovelle.
Long-time behavior in scalar conservation laws, in: Diff. Int. Eq., 2009, vol. 22, n^o 3-4, p. 225-238.

[24]

E. Faou.
Analysis of splitting methods for reaction-diffusion problems using stochastic calculus., in: Math. Comp., 2009, vol. 78, p. 1467–1483.

[25]

E. Faou, B. Grébert, E. Paturel.
Birkhoff normal form for splitting methods applied to semi linear Hamiltonian PDEs. Part I: Finite dimensional discretization, in: Numer. Math., 2009, to appear.

[26]

E. Faou, B. Grébert, E. Paturel.
Birkhoff normal form for splitting methods applied to semi linear Hamiltonian PDEs. Part II: Abstract splitting, in: Numer. Math., 2009, to appear.

[27]

E. Faou, V. Gradinaru, C. Lubich.
Computing semi-classical quantum dynamics with Hagedorn wavepackets, in: SIAM J. Sci. Comp., 2009, vol. 31, p. 3027–3041.

[28]

E. Faou, T. Lelièvre.
Conservative stochastic differential equations: Mathematical and numerical analysis, in: Math. Comp., 2009, vol. 78, p. 2047–2074.

Other Publications

[29]

N. Champagnat, C. Chipot, E. Faou.
A probabilistic approach of high-dimensional least-squares approximations, 2009, Preprint.

[30]

E. Faou, B. Grébert.
Quasi invariant modified Sobolev norms for semi linear reversible PDEs., 2009, Preprint.

[31]

E. Faou, B. Grébert.
Resonances in long time integration of semi linear Hamiltonian PDEs., 2009, Preprint.

References in notes

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A. Bandrauk, E. Dehghanian, H. Lu.
Complex integration steps in decomposition of quantum exponential evolution operators, in: Chem. Phys. Lett., 2006, vol. 419, p. 346–350.

[33]

S. Blanes, F. Casas.
On the necessity of negative coefficients for operator splitting schemes of order higher than two, in: Appl. Num. Math., 2005, vol. 54, p. 23–37.

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J. C. Butcher.
The effective order of Runge-Kutta methods, in: Proceedings of Conference on the Numerical Solution of Differential Equations, J. L. Morris (editor), Lecture Notes in Math., 1969, vol. 109, p. 133–139.

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J. C. Butcher.
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D. Calaque, K. Ebrahimi-Fard, D. Manchon.
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J. E. Chambers.
Symplectic integrators with complex time steps, in: Astron. J., 2003, vol. 126, p. 1119–1126.

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A. Connes, H. Moscovici.
Hopf Algebras, cyclic cohomology and the transverse index theorem, in: Commun. Math. Phys., 1998, vol. 198.

[39]

S. Descombes.
Convergence of a splitting method of high order for reaction-diffusion systems, in: Math. Comp., 2001, vol. 70, n^o 236, p. 1481–1501 (electronic).

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High degree precision decomposition method for the evolution problem with an operator under a split form, in: M2AN Math. Model. Numer. Anal., 2002, vol. 36, n^o 4, p. 693–704.

[41]

Z. Gegechkori, J. Rogava, M. Tsiklauri.
The fourth order accuracy decomposition scheme for an evolution problem, in: M2AN Math. Model. Numer. Anal., 2004, vol. 38, n^o 4, p. 707–722.

[42]

D. Goldman, T. J. Kaper.
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[43]

E. Hairer.
Geometric integration of ordinary differential equations on manifolds, in: BIT, 2001, vol. 41, p. 996–1007.

[44]

E. Hairer, C. Lubich, G. Wanner.
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[45]

E. Hairer, G. Wanner.
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[46]

E. Hairer, G. Wanner.
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[47]

A. Iserles, H. Z. Munthe-Kaas, S. P. Nørsett, A. Zanna.
Lie-group methods, in: Acta Numerica, 2000, p. 215–365.

[48]

D. Kreimer.
On the Hopf algebra structure of perturbative quantum field theory, in: Adv. Theor. Math. Phys., 1998, vol. 2, p. 303–334.

[49]

C. Lubich.
A variational splitting integrator for quantum molecular dynamics, in: Appl. Numer. Math., 2004, vol. 48, p. 355–368.

[50]

C. Lubich.
On variational approximations in quantum molecular dynamics, in: Math.   Comp., 2009, to appear.

[51]

F. A. Potra, W. C. Rheinboldt.
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[52]

H. H. Rosenbrock.
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[53]

J. M. Sanz-Serna, M. P. Calvo.
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[54]

M. Schatzman.
Numerical integration of reaction-diffusion systems, in: Numer. Algorithms, 2002, vol. 31, n^o 1-4, p. 247–269, Numerical methods for ordinary differential equations (Auckland, 2001).

[55]

Q. Sheng.
Solving linear partial differential equations by exponential splitting, in: IMA J. Numer. Anal., 1989, vol. 9, p. 199–212.

[56]

G. J. Sussman, J. Wisdom.
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