Interests
Numerical methods for ordinary and partial differential equations. Geometric numerical integration. Molecular dynamics. Highly oscillatory problems. Wave equations. Exponential integrators. Numerical methods for stochastic (partial) differential equations.
My CV (30.06.17), Google Scholar Profile, and AMS Profile, and ResearchGate Profile, and ORCID Profile



Submitted



Accepted/Published

  • In collaboration with K. Burrage and Y. Komori, Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations, to appear in SIAM J. Sci. Comp, 27.05.2017.

  • In collaboration with D. Furihata, T. Matsuo, Y. Miyatake, Geometric numerical integrators for Hunter--Saxton-like equations, in JJIAM, 12.05.2017. The original publication is available at www.springer.com

  • In collaboration with G. Dujardin, Exponential integrators for nonlinear stochastic Schrödinger equations with white noise dispersion , in Stoch PDE: Anal Comp, 03.04.2017. The original publication is available at www.springer.com

  • In collaboration with R. Anton, Exponential integrators for stochastic Schrödinger equations driven by Ito noise , to appear in the special issue on SPDEs of J. Comput. Math, 2017.

  • In collaboration with R. Anton, S. Larsson, X. Wang Full discretisation of semi-linear stochastic wave equations driven by multiplicative noise, published in SIAM Journal on Numerical Analysis, 12.04.2016. The original publication is available at http://epubs.siam.org

  • In collaboration with O. Verdier, Multi-symplectic discretisation of wave map equations, published in SIAM Journal on Scientific Computing, 23.03.2016. The original publication is available at http://epubs.siam.org

  • In collaboration with C. Chen, J. Hong, Conservative methods for stochastic differential equations with a conserved quantity , pdf format, 26.09.2015, published in International Journal of Numerical Analysis and Modeling. The original publication is available at http://www.math.ualberta.ca/ijnam/

  • In collaboration with L. Quer-Sardanyons, A fully discrete approximation of the one-dimensional stochastic wave equation , pdf format, 28.01.2015, published in IMA Journal of Numerical Analysis. The original publication is available at www.oxfordjournals.org

  • In collaboration with J. Schweitzer, High order numerical methods for highly oscillatory problems , pdf format, 12.11.2014, published in ESAIM:M2AN. The original publication is available at www.esaim-m2an.org

  • In collaboration with L. Gauckler, E. Hairer, Ch. Lubich Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions , pdf format, 15.09.2014, published in BIT. The original publication is available at www.springer.com

  • In collaboration with T. Matsuo, X. Raynaud A multi-symplectic numerical integrator for the two-component Camassa--Holm equation , pdf format, 19.05.2014, published in J. Nonlinear Math. Phys. The original publication is available at www.tandfonline.com

  • In collaboration with G. Dujardin Energy-preserving integrators for stochastic Poisson systems , pdf format, 10.2013, published in Communications in Mathematical Sciences. The original publication is available at http://www.intlpress.com

  • In collaboration with S. Larsson, M. Sigg A trigonometric method for the linear stochastic wave equation , pdf format, 09.2012, published in SIAM Journal on Numerical Analysis. The original publication is available at http://epubs.siam.org

  • In collaboration with A. Abdulle, G. Vilmart, K. Zygalakis High weak order methods for stochastic differential equations based on modified equations , pdf format, 05.2012, published in SIAM Journal on Scientific Computing. The original publication is available at http://epubs.siam.org

  • In collaboration with L. Gauckler One-Stage Exponential Integrators for Nonlinear Schrödinger Equations Over Long Times , pdf format, 04.2012, published in BIT. The original publication is available at www.springerlink.com

  • On the numerical discretisation of stochastic oscillators, pdf format, 03.2012, published in Mathematics and Computers in Simulation. The original publication is available at www.elsevier.com

  • In collaboration with X. Raynaud Convergent numerical schemes for the compressible hyperelastic rod wave equation, pdf format, 12.2011, published in Numerische Mathematik. The original publication is available at www.springerlink.com

  • In collaboration with M. Sigg Convergence analysis of trigonometric methods for stiff second-order stochastic differential equations, pdf format, 11.2011, published in Numerische Mathematik. The original publication is available at www.springerlink.com

  • In collaboration with E. Hairer Linear energy-preserving integrators for Poisson systems, pdf format, 2011, published in BIT Numerical Mathematics. The original publication is available at www.springerlink.com

  • In collaboration with X. Raynaud Geometric finite difference schemes for the generalised hyperelastic-rod wave equation, pdf format, 2010, published in Journal of Computational and Applied Mathematics. The original publication is available at www.sciencedirect.com.

  • In collaboration with E. Hairer and C. Lubich Conservation of energy, momentum and actions in numerical discretizations of nonlinear wave equations, pdf format, 2008, published in Numerische Mathematik. The original publication is available at www.springerlink.com .

  • In collaboration with X. Raynaud and B. Owren Multi-symplectic integration of the Camassa-Holm equation pdf format, July 2008, published in Journal of Computational Physics. The original publication is available at www.sciencedirect.com .

  • In collaboration with E. Hairer and C. Lubich Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions, pdf format, April 2007, is published in Arch. Rat. Mech. Anal. The original publication is available at www.springerlink.com .

  • In collaboration with E. Celledoni and B. Owren Symmetric exponential integrators with an application to the cubic Schrödinger equation, pdf format, November 2007, published in FOCM.

  • In collaboration with T. Jahnke, K. Lorenz and C. Lubich Numerical integrators for highly oscillatory Hamiltonian systems: a review, pdf format, April 2006, published in Analysis, Modeling and Simulation of Multiscale Problems, A. Mielke (ed.), Springer, Berlin, 2006.

  • Conservation properties of numerical integrators for highly oscillatory Hamiltonian systems, pdf format, 2005, published in IMA Journal of Numerical Analysis .

  • My PHD dissertation Analysis and Numerical Treatment of Highly Oscillatory Differential Equations, pdf format,2004.
    Another link for this document: CYBERTHESE. You can also find all the PHD thesis published (electronically) in Geneva.

  • In collaboration with E. Hairer and C. Lubich Numerical energy conservation for multi-frequency oscillatory differential equations, pdf format, published in BIT , 2005 (vol. 45, no. 2, pp. 287--305).

  • In collaboration with E. Hairer and C. Lubich Modulated Fourier expansions of highly oscillatory differential equations, pdf format, published in FOCM , 2003.

  • My diploma thesis (pdf format). It's in french and it deals with assymptotic development of highly oscillatory differential equations.



    History/Preprints
  • 03.2012. In collaboration with D. Furihata, T. Matsuo, Y. Miyatake, Geometric numerical integrators for Hunter--Saxton-like equations, submitted, 03.12.2013.
  • 03.2012. In collaboration with G. Dujardin, Energy-preserving integrators for stochastic Poisson systems, submitted, 25.02.2013.
  • 03.2012. In collaboration with S. Larsson and M. Sigg, A trigonometric method for the linear stochastic wave equation, submitted, 16.03.2012. arXiv.org pdf.
  • 09.2011. In collaboration with A. Abdulle, G. Villmart, and K.C. Zygalakis, High order weak methods for stochastic differential equations based on modified equations, 09.2011.
  • 07.2011. In collaboration with L. Gauckler, Exponential integrators for nonlinear Schroedinger equations over long times, 07.2011.
  • 05.2011. In collaboration with X. Raynaud, Convergent Numerical Schemes for the Compressible Hyperelastic Rod Wave Equation, 05.2011.
  • 01.2011. In collaboration with M. Sigg, Convergence analysis of trigonometric methods for stiff second-order stochastic differential equations, 01.2011.
  • 04.2010. In collaboration with E. Hairer Linear energy-preserving integrators for Poisson systems, submitted, 04.2010.
  • 02.2010. A note on the numerical discretisation of stochastic oscillators, submitted, 02.2010.
  • 09.2009. A note on stochastic oscillators, in preparation, September 2009.
  • 09.2009. Revised version of "Geometric finite difference schemes for the generalised hyperelastic-rod wave equation", September 2009.
  • 09.2009. SNF-Project: "Numerical methods for stochastically driven wave equations" (3 years).
  • 09.2008. In collaboration with Xavier Raynaud Geometric finite difference schemes for the generalised hyperelastic-rod wave equation pdf format, September 2008.
  • 04.2008. In collaboration with Xavier Raynaud and Brynjulf Owren Multi-symplectic integration of the Camassa-Holm equation pdf format, July 2007, published in Journal of Computational Physics. The original publication is available at www.sciencedirect.com
  • 11.2007. The paper Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions, pdf format, April 2007, is published in Arch. Rat. Mech. Anal. The original publication will be available at www.springerlink.com .
  • 11.2007. Symmetric exponential integrators with an application to the cubic Schrödinger equation, pdf format, November 2007, published in FOCM.
  • 08.2007. New version of the paper Symmetric exponential integrators with an application to the cubic Schrödinger equation, pdf format, August 2007, submitted.
  • 07.2007. In collaboration with Xavier Raynaud and Brynjulf Owren Multi-symplectic integration of the Camassa-Holm equation, pdf format, July 2007, submitted.
  • 04.2007. A new version of the paper Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions, pdf format, April 2007.
    And for the numerical discretization Conservation of energy, momentum and actions in numerical discretizations of nonlinear wave equations, pdf format, April 2007, submitted.
  • 11.2006. First paper from Trondheim !! In collaboration with Elena Celledoni and Brynjulf Owren Symmetric exponential integrators for the cubic Schrödinger equation, pdf format, November 2006, submitted.
  • 10.2006. For my first talk in Trondheim, I did a kind of panoramic overview on Hamiltonian oscillatory porblems. You can find the pdf file of my talk by following this link TRONDHEIM.pdf, pdf format, October 2006.
  • 05.2006. In collaboration with Ernst Hairer and Christian Lubich, Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions, pdf format, May 2006, submitted to Arch. Rat. Mech. Anal.
  • 04.2006. Numerical integrators for highly oscillatory Hamiltonian systems: a review, pdf format, April 2006, published in Analysis, Modeling and Simulation of Multiscale Problems, A. Mielke (ed.), Springer, Berlin, 2006. A nice review written with Tobias Jahnke, Katina Lorenz and Christian "the boss" Lubich.
  • 01.2005. Conservation properties of numerical integrators for highly oscillatory Hamiltonian systems, pdf format, 2005, published in IMA Journal of Numerical Analysis .
  • 12.2004. A little ANIMATION of a planar dumbbell spacecraft. I used my numerical method (NTM) on an example taken from an article of Jinglai SHEN. I want also to thanks Emil Mikulic for his tga2avi program.
  • 06.2004. My PHD dissertation Analysis and Numerical Treatment of Highly Oscillatory Differential Equations, pdf format,2004.
    Another link for this document: CYBERTHESE. You can also find all the PHD thesis published (electronically) in Geneva.
  • 03.2004. We add some frequencies, and obtain, still with the tandem E.Hairer and C.Lubich : Numerical energy conservation for multi-frequency oscillatory differential equations, pdf format, published in BIT , 2005 (vol. 45, no. 2, pp. 287--305).
  • ??.2003. In collaboration with C.Lubich and E.Hairer : Modulated Fourier expansions of highly oscillatory differential equations, pdf format, published in FOCM , 2003.
  • 05.2000. Here is my diploma thesis (pdf format). It's in french and it deals with assymptotic development of highly oscillatory differential equations.


  • "Research is when you don't know what you're doing", F.S. ACTON.


    last modifications: 30.06.17