Interests
Numerical methods for ordinary and partial differential equations. Numerical methods for stochastic (partial) differential equations. Geometric numerical integration.
My CV (09.04.24), Google Scholar Profile, and AMS Profile, and ResearchGate Profile, and ORCID Profile


Submitted

  • In collaboration with M. Cai and X. Wang Strong convergence rates for a full discretization of stochastic wave equation with nonlinear damping, submitted, 06.07.2023 (arXiv).

  • In collaboration with C-E. Bréhier and J. Ulander Analysis of a positivity-preserving splitting scheme for some nonlinear stochastic heat equations, submitted, 20.02.2023 (arXiv).

    Accepted/Published

  • In collaboration with C-E. Bréhier Splitting integrators for linear Vlasov equations with stochastic perturbations, submitted, 12.07.2023. To appear in Journal of Computational Dynamics, 27.02.2024. The original publication is available at tba.

  • In collaboration with C-E. Bréhier and G. Giordano Splitting schemes for FitzHugh--Nagumo stochastic partial differential equations, submitted, 17.09.2022 (arXiv). Publihed in Discrete and Continuous Dynamical Systems B, 10.05.2023. The original publication is available at www.aimsciences.org/dcdsb.

  • In collaboration with C-E. Bréhier and J. Ulander Positivity-preserving schemes for some nonlinear stochastic PDEs, submitted, 20.02.2023. To appear in the proceedings of the Sixteenth International Conference Zaragoza-Pau on Mathematics and its Applications 2022, 31.03.2023.

  • In collaboration with A. Berg and G. Dujardin, Approximated exponential integrators for the stochastic Manakov equation, submitted, 12.05.2020 (arXiv). Published in Journal of Computational Dynamics, 10.03.2023. The original publication is available at www.aimsciences.org/jcd.

  • In collaboration with C-E. Bréhier and T. Jahnke Splitting integrators for stochastic Lie-Poisson systems, submitted, 16.11.2021 (arXiv). Publihed in Mathematics of Computation, 14.01.2023. The original publication is available at www.ams.org.

  • In collaboration with C-E. Bréhier, Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations, submitted, 15.11.2022 (arXiv). Published in Applied Numerical Mathematics, 05.01.2023. The original publication is available at www.sciencedirect.com.

  • In collaboration with A. Lang, Numerical approximation and simulation of the stochastic wave equation on the sphere, submitted, 09.02.2021 (arXiv). Published Calcolo, 01.08.2022. The original publication is available at www.link.springer.com.

  • In collaboration with C-E. Bréhier, Strong rates of convergence of a splitting scheme for Schrödinger equations with nonlocal interaction cubic nonlinearity and white noise dispersion, submitted, 03.11.2020 (arXiv). Published SIAM/ASA JUQ, 01.04.2022. The original publication is available at epubs.siam.org.

  • In collaboration with A. Berg and G. Dujardin, Lie--Trotter splitting for the nonlinear stochastic Manakov system, submitted, 22.10.2020 (arXiv). Published Journal of Scientific Computing, 22.05.2021. The original publication is available at www.link.springer.com.

  • In collaboration with G. Vilmart, Drift-preserving numerical integrators for stochastic Poisson systems, submitted, 28.05.2020 (arXiv). Published in International Journal of Computer Mathematics, 21.05.2021. The original publication is available at www.tandfonline.com.

  • In collaboration with K. Debrabant and A. Rößler, High order numerical integrators for single integrand Stratonovich SDEs, submitted, 06.04.2020 (arXiv). Published in Applied Numerical Mathematics, 10.08.2020. The original publication is available at www.sciencedirect.com.

  • In collaboration with J. Cui, J. Hong and L. Sun, Exponential Integrators for Stochastic Maxwell's Equations Driven by Ito Noise, published in J. Comput. Phys., 03.03.2020. The original publication is available at www.sciencedirect.com.
    The codes for the numerical experiments of this manuscript can be found here .

  • In collaboration with C. Chen, R. D'Ambrosio and A. Lang, Drift-preserving numerical integrators for stochastic Hamiltonian systems, published in Adv Comput Math., 20.01.2020. The original publication is available at www.link.springer.com.

  • In collaboration with R. Anton and L. Quer-Sardanyons, A fully discrete approximation of the one-dimensional stochastic heat equation, published in IMA Journal of Numerical Analysis, 28.08.2018. The original publication is available at www.oxfordjournals.org.

  • Numerical discretisations of stochastic wave equations, published in AIP Conference Proceedings, 22.07.2018. The original publication is available at www.aip.scitation.org.

  • In collaboration with R. Anton, Exponential integrators for stochastic Schrödinger equations driven by Ito noise , published in the special issue on SPDEs of J. Comput. Math, 12.02.2018. The original publication is available at www.global-sci.org.

  • In collaboration with K. Burrage and Y. Komori, Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations, published in SIAM J. Sci. Comp, 12.12.2017. The original publication is available at www.epubs.siam.org

  • In collaboration with D. Furihata, T. Matsuo, Y. Miyatake, Geometric numerical integrators for Hunter--Saxton-like equations, published 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 , published in Stoch PDE: Anal Comp, 03.04.2017. The original publication is available at www.springer.com and here.

  • 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. Vilmart, 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: 09.04.24