Publications in Journals

  1. Ibrahim Almuslimani, Philippe Chartier, Mohammed Lemou, Florian Méhats, Uniformaly accurate schemes for oscillatory stochastic differential equations, 2021, to be submitted.
  2. François Castella, Philippe Chartier, Julie Sauzeau. Analysis of a time-dependent problem of mixed migration and population dynamics, 2021, to be submitted
  3. Philippe Chartier, Ander Murua. Majorants series for the N-body problem, to appear in International Journal of Computer Mathematics, 2021.
  4. Sergio Blanes, Fernando Casas, Philippe Chartier, Alejandro Escorihuela-Tomàs. On symmetric-conjugate composition methods in the numerical integration of differential equations, in revision, 2021.
  5. Philippe Chartier, Mohammed Lemou, Léopold Trémant, Uniformly accurate numerical schemes for a class of dissipative systems, to appear in Mathematics of Computation, 2021.
  6. Philippe Chartier, Mohammed Lemou, Florian Méhats, Xiaofei Zhao, Derivative-free high-order uniformly accurate schemes for highly-oscillatory systems, to appear in IMA Journal of Numerical Analysis, 2021.
  7. Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou, Florian Méhats. An averaging technique for transport equations, Kinetic and Related Models, December  2020, 13(6): 1107-1133. doi: 10.3934/krm.2020039.
  8. Mikel Antoñana, Philippe Chartier, Joseba Makazaga, Ander Murua, Global time-regularisation of the gravitational N-body problemto appear in SIAM Journal on Applied Dynamical Systems, 2020.
  9. Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou, Florian Méhats, Xiaofei Zhao, Uniformly accurate methods for three dimensional Vlasov equations with strong magnetic field under varying direction, to appear in SIAM Journal on Scientific Computing, 2020.
  10. Fernando Casas, Philippe Chartier, Alejandro Escorihuela, Yong Zhang, Compositions of pseudo-symmetric integrators with complex coefficients for the numerical integration of differential equations, Journal of Computational and Applied Mathematics, online, 2020.
  11. Philippe Chartier, Mohammed Lemou, Florian Méhats, Gilles Vilmart. A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations, Foundations of Computational Mathematics, Vol 20, Feb., 2020.
  12. Fernando Casas, Philippe Chartier, Ander Murua, Continuous changes of variables and the Magnus expansion, J, , ,  2019.
  13. Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou, Florian Méhats, Xiaofei Zhao. Uniformly accurate methods for Vlasov equations with non-homogeneous strong magnetic field, Mathematics of Computation 88, 2697-2736, American Mathematical Society, 2019.
  14. Philippe Chartier, Mohammed Lemou, Florian Méhats, Gilles Vilmart. Highly-oscillatory problems with time-dependent vanishing frequency, SIAM Journal on Numerical Analysis, 57(2), 925–944, 2019.
  15. Philippe Chartier, Loïc Le Treust, Florian Méhats. Uniformly accurate time-splitting methods for the semiclassical linear Schrödinger equation, M2AN, Vol. 53, Number 2, 2019.
  16. Philippe Chartier, Nicolas Crouseilles, Xiaofei Zhao. Numerical methods for the two-dimensional Vlasov–Poisson equation in the finite Larmor radius approximation regime, Journal of Computational Physics, Elsevier, 2018, 375, pp.619-640.
  17. François Castella, Philippe Chartier, Julie Sauzeau. A formal series approach to the center manifold theorem, Foundations of Computational Mathematics, Springer Verlag, 2018, 18 (6), pp.1397-1434.
  18. Philippe Chartier, Mohammed Lemou, Florian Méhats. Highly-oscillatory evolution equations with multiple frequencies: averaging and numerics, Numerische Mathematik, Springer Verlag, 2017, 136 (4), pp.907-939.
  19. Philippe Chartier, Florian Méhats, Mechthild Thalhammer, Yong Zhang. Convergence of multi-revolution composition time-splitting methods for highly oscillatory differential equations of Schrödinger type, M2AN, EDP Sciences, 2017, 51 (5), pp.1859 - 1882.
  20. Philippe Chartier, Norbert J. Mauser, Florian Méhats, Yong Zhang. Solving highly-oscillatory NLS with SAM: numerical efficiency and geometric properties, Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2016, 9 (5), pp.1327-1349.
  21. Philippe Chartier, Florian Méhats, Mechthild Thalhammer, Yong Zhang. Improved error estimates for splitting methods applied to highly-oscillatory nonlinear Schrödinger equations, Mathematics of Computation, American Mathematical Society, 2016, 85 (302), pp.2863-2885.
  22. François Castella, Philippe Chartier, Florian Méhats, Ander Murua. Stroboscopic Averaging for the Nonlinear Schrödinger Equation, Foundations of Computational Mathematics, Springer Verlag, 2015, 15 (2), pp.519-559.
  23. Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou and Florian Méhats, Uniformly accurate numerical schemes for highly oscillatory Klein-Godon and nonlinear Schrödinger equation, Numerische Mathematik, Vol. 129, Issue 2, pp 211-250, February 2015. 
  24. Philippe Chartier, Ander Murua, Jesus Maria Sanz-Serna. Higher-order averaging, formal series and numerical integration III: error bounds, Foundations of Computational Mathematics, Springer Verlag, 2015, 15 (2), pp.591-612.
  25. Philippe Chartier, Joseba Makazaga, Ander Murua, and Gilles Vilmart, Multi-revolution composition methods for highly oscillatory differential equations, Numerische Mathematik,  Vol. 128, No. 1, pp 167-192, 2014.
  26. Philippe Chartier, Ander Murua and Jesus-Maria Sanz-Serna, Higher-order averaging, formal series and numerical integration III: error bounds,  Foundations of Computational Mathematics, Springer Verlag,  DOI: 10.1007/s10208-013-9175-7, 2013.
  27. P. Chartier, Symmetric Methods, Encyclopedia of Applied and Computational Mathematics, Springer, 2013.
  28. Sergio Blanes, Fernando Casas, Philippe Chartier, Ander Murua. Optimized high-order splitting methods for some classes of parabolic equations, Mathematics of Computation, American Mathematical Society, 2013, 82 (283), pp.1559-1576.
  29. Philippe Chartier, Ander Murua and Jesus-Maria Sanz-Serna, A formal series approach to averaging: exponentially small error estimates, Discrete and Continuous Dynamical Systems (DCDS-A), Vol. 32, no. 9, 2012.
  30. Philippe Chartier, Ander Murua and Jesus-Maria Sanz-Serna, Higher-order averaging, formal series and
    numerical integration II: the quasi-periodic case    ,  Foundations of Computational Mathematics, Springer Verlag, DOI: 10.1007/s10208-012-9118-8, 2012.
  31. Mari-Paz Calvo, Philippe Chartier, Ander Murua and Jesus-Maria Sanz-Serna, Numerical experiments with the stroboscopic method, Applied Numerical Mathematics, Vol. 61 (2011), 1077-1095. 
  32. Mari-Paz Calvo, Philippe Chartier, Ander Murua and Jesus-Maria Sanz-Serna, 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.
  33. P. Chartier, A. Murua and J.M. Sanz-Serna, Higher-order averaging, formal series and
    numerical integration I: B-series    ,  Foundations of Computational Mathematics, Vol. 10, No. 6, 2010.
  34. 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.
  35. P. Chartier, E. Hairer and G. Vilmart, Algebraic structures of B-series,   Foundations of Computational Mathematics, Vol. 10, No. 4, 2010.
  36. P. Chartier and A. Murua, An algebraic theory of order, M2AN, Vol. 43 No. 4, 2009. 
  37. F. Castella, P. Chartier and E. Faou,  An averaging technique for highly-oscillatory Hamiltonian problems, SIAM Journal on Numerical Analysis, Volume 47, Issue 4, 2009.
  38. 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.  
  39. P. Chartier and E. Faou,  Volume-energy preserving integrators for piecewise smooth approximations of Hamiltonian systems, M2AN, Vol. 42, No. 2, 2008.
  40. 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.
  41. P. Chartier, E. Hairer, and G. Vilmart, Numerical integrators based on modified differential equations,  Mathematics of Computation, 2007, Vol. 76 : 260. 
  42. P. Chartier, E. Hairer and G. Vilmart, Modified differential equations,  ESAIM Proceedings, Vol. 21, 2007.
  43. P. Chartier and A. Murua, Preserving first integrals and volume forms of additively split systems, IMA Journal of Numerical Analysis,  2007, Vol. 27:2. 
  44. 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.
  45. 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.
  46. 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
  47. F. Castella, P. Chartier, and E. Faou , Raman Laser Modeling: Mathematical and Numerical Analysis, M2AN, Vol. 38 No. 3, 2004.
  48. 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.
  49. 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.
  50. 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.
  51. F. Castella, P. Chartier, and E. Faou , Analysis of a Poisson system with boundary conditions,  C. R. Acad. Sci. Paris, Ser. I 336, 2003.
  52. R.P.K. Chan , P. Chartier and A. Murua, Post-projected Runge-Kutta methods for index-2 differential-algebraic equations, Applied Numerical Mathematics, Vol. 42, 2002.
  53. 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.
  54. 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.
  55. 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. 
  56. A. Aubry and P. Chartier, On Improving the Convergence of Radau IIA methods when Applied to Index-2 DAEs, SIAM Journal on Numerical Analysis, Vol. 35, No. 4, 1998.
  57. A. Aubry and P. Chartier, Pseudo-symplectic Runge-Kutta Methods, BIT, Vol. 38, No. 3, pp. 229-246, 1998.
  58. 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.
  59. A. Aubry and P. Chartier, A note on pseudo-symplectic Runge-Kutta methods, BIT, Vol. 38 , No. 4, 1998.
  60. P. Chartier, The potential of parallel multi-value methods for the simulation of large real-life problems, CWI Quaterly, Vol. 11, No.1, 1998.
  61. 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.
  62. J.C. Butcher, P. Chartier and Z. Jackiewicz, Nordsieck representation of DIMSIMs, Numerical Algorithms, Vol. 16, No. 2, pp. 209-230, 1997.
  63. 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.
  64. 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.
  65. 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.
  66. P. Chartier, L-Stable Parallel One-Block Methods for Ordinary Differential Equations, SIAM Journal on Numerical Analysis, Vol. 31, No. 2, pp. 552-571, April 1994.
  67. P. Chartier and B. Philippe, A Parallel Shooting Technique for Solving Dissipative ODEs, Computing, Vol. 51, No. 3-4, 1993. 

Proceedings

  1. P. Chartier, A. Murua and J.M. Sanz-Serna, A New Approach to High-Order Averaging, AIP (American Institute of Physics) Conference Proceedings
  2. P. Chartier, A. Murua and J.M. Sanz-Serna, Stroboscopic averaging in Banach spaces: application to NLS, AIP (American Institute of Physics) Conference Proceedings. 
  3. P. Chartier and E. Faou, A numerical method for Hamiltonian systems based on piecewise smooth space-approximations, Mathematisches Forschunginstitut Oberwolfach Report No. 14/2006.
  4. A. Aubry et P. Chartier, Pseudo-symplectic Runge-Kutta methods, Proceedings of the Anode Conference, Auckland, New-Zealand, July 1998.
  5. P. Chartier, On diagonally-iterated Runge-Kutta methods for dissipative ODEs, 15th IMACS World Congress, Berlin, Allemagne, August 25-30, 1997.
  6. 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.
  7. 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.
  8. 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.


Theses and research reports

  1. 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.
  2. 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.
  3. 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.
  4. P. Chartier and E. Lapôtre, Reversible B-series, INRIA report No. 1221, 1998.
  5. P. Chartier, E. Hairer and G. Vilmart, A substitution law for B-series vector fields, INRIA report No. 5498, 2005.