Publications in Journals
- F.
Castella, P. Chartier, F. Méhats and A. Murua, Stroboscopic averaging for the Schrödinger equation, in preparation.
- S. Blanes, F. Casas, P. Chartier and A. Murua, Splitting methods with complex coefficients for some classes of evolution equations, Math. Comput. In Press. arXiv:1102.1622v1.
- P. Chartier, J.M. Sanz-Serna and A. Murua, Higher-order averaging, formal series and
numerical integration II: the quasi-periodic case, submitted.
- M.P. Calvo, P. Chartier, J.M. Sanz-Serna and A. Murua, Numerical experiments with the stroboscopic method, Appl. Numer. Math. 61 (2011), 1077-1095.
- M.P. Calvo, P. Chartier, J.M. Sanz-Serna and A. Murua, A stroboscopic numerical method for highly
oscillatory problems, in Numerical Analysis
and Multiscale Computations, B. Engquist, O. Runborg and R. Tsai,
editors, Lect. Notes Comput. Sci. Eng., Vol. 82, Springer 2011, 73-87.
- P. Chartier, J.M. Sanz-Serna and A. Murua, Higher-order averaging, formal series and
numerical integration I: B-series, FOCM, Vol. 10, No. 6, 2010.
- P. Chartier, E. Darrigrand and E.
Faou, A
Fast Multipole Method for Geometric Numerical Integrations of
Hamiltonian Systems (Part I and Part II), BIT Numerical Mathematics, Vol. 50, No. 1, 2010.
- P. Chartier, E.
Hairer and G.
Vilmart, Algebraic structures of B-series, FOCM, Vol. 10, No. 4, 2010.
- P. Chartier and A. Murua, An
algebraic theory of order, M2AN, Vol. 43 No. 4, 2009.
- F. Castella, P. Chartier and E.
Faou, An
averaging technique for highly-oscillatory Hamiltonian problems, SIAM J. Numer. Anal. Volume 47, Issue 4, 2009.
- F.
Castella, P. Chartier, S. Descombes
and G. Vilmart,
Splitting
methods with complex times for parabolic equations, BIT Numerical Mathematics, Vol. 49, No. 3, 2009.
- P. Chartier and E.
Faou, Volume-energy
preserving
integrators for piecewise smooth approximations of Hamiltonian systems, M2AN, Vol. 42,
No. 2, 2008.
- P. Chartier and E.
Faou, A
simple proof of the existence of adiabatic invariants for perturbed
reversible systems, J. Phys. A: Math. Theor. 41 No 47, 2008.
- P. Chartier, E.
Hairer, and G.
Vilmart, Numerical
integrators based on modified differential equations,
Mathematics of
Computation, 2007, Vol. 76 : 260.
- P. Chartier, E.
Hairer and G. Vilmart, Modified
differential equations, ESAIM
Proceedings, Vol. 21, 2007.
- P. Chartier and A. Murua, Preserving first
integrals and
volume forms of additively split systems, IMA
Journal of Numerical Analysis 2007, Vol. 27:2.
- P. Chartier, E.
Faou and A. Murua, An algebraic approach
to
invariant preserving integrators: The case of quadratic and Hamiltonian
invariants, Numerische
Mathematik, Vol. 103, 2006.
- E.
Cancès, F.
Castella, P. Chartier, E. Faou,
C.
Le Bris, F. Legoll and
G.
Turinici, Long-time
averaging using symplectic
solvers with application to molecular dynamics, Numerische
Mathematik, Vol. 100, 2005.
- R.P.K.
Chan , P. Chartier and A. Murua, Reversible methods of
Runge-Kutta
type for Index-2 Differential-Algebraic Equations, Numerische
Mathematik,Vol. 97, No. 3, 2004
- F.
Castella, P. Chartier, and E. Faou
, Raman Laser
Modeling: Mathematical and
Numerical Analysis, Mathematical
Modelling and Numerical Analysis, Vol. 38 No. 3, 2004.
- E.
Cancès, F.
Castella,
P. Chartier, E.
Faou, C.
Le Bris, F. Legoll
and G.
Turinici, High-order
averaging schemes with error bounds for thermodynamical properties
calculations by MD simulations, Journal
of Chemical Physics, Vol. 121 (21) 10346-10355, 2004.
- Florence Leplingard, Catherine Martinelli,
Sophie Borne, Laurence Lorcy, Thierry Lopez, Dominique Bayart,
François Castella, Philippe Chartier, and Erwan Faou, Modeling
of
multi-wavelength Raman fiber lasers using a new and fast algorithm,
IEEE
Photonics Technology Letters, Vol. 16, No. 12, 2004.
- F.
Bonnans,
P. Chartier and H.
Zidani, Discrete approximation of the
Hamilton-Jacobi equation
for a control system of a differential-algebraic system, Control
and Cybernetics, Vol. 32, No.1, 2003.
- F.
Castella, P. Chartier, and E. Faou
, Analysis of
a Poisson system with
boundary conditions, C.
R. Acad.
Sci. Paris, Ser. I 336, 2003.
- R.P.K.
Chan , P. Chartier and A. Murua, Post-projected
Runge-Kutta
methods for index-2 differential-algebraic equations, Appl.
Numer. Math.., Vol. 42, 2002.
- R.P.K.
Chan and P. Chartier, Classification of High-Order
Implicit
Runge-Kutta Methods by Characterization of their Properties, New-Zealand
Journal of Mathematics,Vol. 29, 2000.
- J.C.
Butcher and P. Chartier, The effective order of
singly-implicit
Runge-Kutta methods, Numerical
Algorithms, Vol.
20, No.
4, pp. 269-284, 1999.
- J.C.
Butcher, P. Chartier and Z.
Jackiewicz, Experiments with a variable-order type
1 DIMSIM code, Numerical
Algorithms, Vol.
22,
No. 3,4, pp. 237-261, 1999.
- A. Aubry and P. Chartier, On Improving the
Convergence of
Radau IIA methods when Applied to Index-2 DAEs, SIAM J.
Numer.
Anal., Vol.
35, No. 4, 1998.
- A. Aubry and P. Chartier, Pseudo-symplectic
Runge-Kutta
Methods, BIT,
Vol.
38, No. 3,
pp. 229-246, 1998.
- P. Chartier, On diagonally-iterated Runge-Kutta
methods
for dissipative ODEs, J.
of Comp. and Appl. Math., Vol.
89, No. 1, pp. 73-85, 1998.
- A. Aubry and P. Chartier, A note on
pseudo-symplectic
Runge-Kutta methods, BIT,
Vol. 38 , No. 4, 1998.
- P. Chartier, The potential of parallel
multi-value methods
for the simulation of large real-life problems, CWI
Quaterly, Vol. 11, No.1, 1998.
- J.C.
Butcher and P. Chartier, A generalization of
singly-implicit
Runge-Kutta methods, J.
of Appl. Numer. Math., Vol. 24, No. 2-3, 1997.
- J.C.
Butcher, P. Chartier and Z.
Jackiewicz, Nordsieck representation of DIMSIMs,
Numerical
Algorithms,
Vol. 16, No. 2, pp. 209-230, 1997.
- R.P.K.
Chan and P. Chartier, A Composition Law for
Runge-Kutta Methods
Applied to Index-2 Differential Algebraic Equations, BIT, Vol. 36, No.
2, pp. 229-246,
1996.
- A. Aubry and P. Chartier, On the structure of
errors for
Radau IA methods applied to index-2 DAEs, J.
of Appl. Numer. Math., Vol. 22, No. 1-3, 1996.
- J.C.
Butcher and P. Chartier, Parallel general linear
methods for
stiff ordinary differential and differential algebraic equations,
J.
of Appl. Numer. Math., Vol. 17, No. 3, pp. 213-222, 1995.
- P. Chartier, L-Stable Parallel One-Block Methods
for
Ordinary Differential Equations, SIAM J.
Numer.
Anal., Vol.
31, No. 2, pp. 552-571, April 1994.
- P. Chartier and B. Philippe, A Parallel Shooting
Technique
for Solving Dissipative ODEs, Computing,
Vol. 51, No. 3-4, 1993.
Proceedings
- P. Chartier, Application of Bellen's Parallel Method to ODE's
with Dissipative Right-Hand Side, Proceedings of the 10th International
Conference on Computing Methods in Applied Science and Engineering,
Paris, France, February 11-14, 1992.
- P. Chartier et B. Philippe,
L-Stable Parallel One-Block Methods for Stiff ODE's, Proceedings of the
sixth SIAM Conference on Parallel Processing for Scientific Computing,
Norfolk, Virginia, USA, March 22-23, 1993.
- J.C. Butcher
and P. Chartier, Parallel general linear methods for stiff
ordinary differential and differential algebraic equations, Proceedings
of the 14th IMACS World Congress on Computational and Applied
Mathematics, Atlanta, Georgia, USA, July 11-15, 1994.
- P. Chartier, On diagonally-iterated Runge-Kutta methods for
dissipative ODEs, 15th IMACS World Congress, Berlin,
Allemagne, August 25-30, 1997.
- A. Aubry et P. Chartier, Pseudo-symplectic Runge-Kutta
methods, Proceedings of the Anode Conference, Auckland, New-Zealand,
July 1998.
- P. Chartier and E. Faou, A
numerical method for Hamiltonian systems based on piecewise smooth
space-approximations, Mathematisches Forschunginstitut Oberwolfach
Report No. 14/2006.
Theses and research reports
- P. Chartier, Parallelism in the Numerical
Solution of
Initial Value Problems in Differential and Differential Algebraic
Equations, Thesis
No. 981, University
of
Rennes
I, June 1993.
- P. Chartier, Méthodes
numériques pour les équations
différentielles
ordinaires et algébriques avec application aux
systèmes
hamiltoniens, Habilitation à
diriger des
recherches, Institut Mathématique de Rennes,
Université
de Rennes 1, 2000.
- J.C.
Butcher and P. Chartier, The
construction of DIMSIMs for stiff ODEs and DAEs,
Report Series
No. 308, July 1994, University
of Auckland, New Zealand.
- P. Chartier and E. Lapôtre, Reversible
B-series, INRIA report No. 1221, 1998.
- P. Chartier, E. Hairer and G. Vilmart, A substitution
law for
B-series vector fields, INRIA report No. 5498, 2005.