List of preprints

NOTE: The list of monographs is on a separate page.
2025
  • Severiano González-Pinto, Ernst Hairer, and Domingo Hernández-Abreu, Interpolation preservation of AMF-W methods for linear diffusion problems , Submitted for publication Abstract
  • Nicola Guglielmi and Ernst Hairer, Solving Delay Differential Equations , Chapter of the book ``Volume 2. Non linear Dynamics. Numerical Methods'' (2025)
  • Nicola Guglielmi and Ernst Hairer, Applying stiff integrators for ODEs and DDES to problems with distributed delays SIAM J. Sci. Comput. 47(1) (2025) A102-A123 Abstract,
    2024
  • Severiano González-Pinto, Ernst Hairer, and Domingo Hernández-Abreu, PDE-convergence in Euclidean norm of AMF-W methods for multidimensional parabolic problems , ESAIM: M2AN 58 (2024) 2119-2133 Abstract
    2023
  • Ernst Hairer, Christian Lubich and Yanyan Shi, Leapfrog methods for relativistic charged-particle dynamics , SINUM 61(6) (2023) 2844-2858 Abstract
  • Nicola Guglielmi and Ernst Hairer, Sliding modes of high codimension in piecewise-smooth dynamical systems , Numerical Algorithms 94 (2023) 257-273 Abstract
  • Severiano González-Pinto, Ernst Hairer, and Domingo Hernández-Abreu, High order PDE-convergence of AMF-W methods for 2D-linear parabolic problems , J. Comput. Appl. Math. 417 (2023) 114642 Abstract
  • Ernst Hairer and Christian Lubich, Large-stepsize integrators for charged particles in a strong magnetic field , Extended abstract, ICNAAM 2021, Rhodes, Greece. AIP Conference Proceedings 2849, 020003 (2023)
    2022
  • Ernst Hairer, Christian Lubich and Yanyan Shi, Large-stepsize integrators for charged-particle dynamics over multiple time scales , Numerische Mathematik 151 (2022) 659-691 Abstract
  • Nicola Guglielmi and Ernst Hairer, An efficient algorithm for solving piecewise-smooth dynamical systems , Numerical Algorithms 89 (2022) 1311-1334 and here . Abstract
    2021
  • Severiano González-Pinto, Ernst Hairer, and Domingo Hernández-Abreu, Power boundedness in the maximum norm of stability matrices for ADI methods , BIT Numer Math 61 (2021) 805-827 and here . Abstract
    2020
  • Ernst Hairer, Christian Lubich, and Bin Wang, A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field , Numerische Mathematik 144 (2020) 787-809 Abstract
  • Severiano González-Pinto, Ernst Hairer, and Domingo Hernández-Abreu, Convergence in l_2 and l_∞ norm of one-stage AMF-W-methods for parabolic problems , SIAM J. Numer. Anal. 58 (2020) 1117-1137 Abstract
  • Ernst Hairer and Christian Lubich, Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field , Numerische Mathematik 144 (2020) 699-728 Abstract
    2019
  • Walter Gautschi and Ernst Hairer, On conjectures of Stenger in the theory of orthogonal polynomials , Journal of Inequalities and Applications (2019) Paper No. 159, 27 Abstract
    2018
  • Nicola Guglielmi and Ernst Hairer, On the limit solution of regularized piecewise-smooth dynamical systems , Technical Reoprt. Abstract
  • Ernst Hairer and Christian Lubich, Energy behaviour of the Boris method for charged-particle dynamics , BIT 58 (2018) 969-979 Abstract
  • Severiano González-Pinto, Ernst Hairer, Domingo Hernández-Abreu and Soledad Pérez-Rodríguez, AMF-type W-methods for parabolic problems with mixed derivatives , SIAM J. Sci. Comput. 40(5) (2018) A2905-A2929 Abstract, Fortran code
  • Ludwig Gauckler, Ernst Hairer, and Christian Lubich, Dynamics, numerical analysis, and some geometry , Proceedings of ICM 2018 (Christian Lubich's plenary talk) Abstract
  • Severiano González-Pinto, Ernst Hairer, Domingo Hernández-Abreu and Soledad Pérez-Rodríguez, PDE-W-methods for parabolic problems with mixed derivatives , Numerical Algorithms 78(3) (2018) 957-981 Abstract
    2017
  • Ernst Hairer and Christian Lubich, Symmetric multistep methods for charged particle dynamics , SMAI J. Comput. Math. 3 (2017) 205-218. Abstract
  • Ernst Hairer and Arieh Iserles, Banded, stable, skew-symmetric differentiation matrices of high order , IMA J. Numer. Anal. 37(3) (2017) 1087-1103. Extended abstract (ICNAAM 2016). Abstract
  • Nicola Guglielmi and Ernst Hairer, Solutions leaving a codimension-2 sliding , Nonlinear Dynamics 88(2) (2017) 1427-1439. Abstract
    2016
  • Ludwig Gauckler, Ernst Hairer, and Christian Lubich, Long-term analysis of semilinear wave equations with slowly varying wave speed , Comm. Partial Differ. Equations 41(12) (2016) 1934-1959. Abstract
  • Ernst Hairer and Christian Lubich, Long-term analysis of the Stoermer-Verlet method for Hamiltonian systems with a solution-dependent high frequency , Numerische Mathematik 34 (2016) 119-138. Abstract
  • Nicola Guglielmi and Ernst Hairer, Path-regularization of linear neutral delay differential equations with several delays , J. Comput. Appl. Math. 292 (2016) 785-794. Abstract
  • Ernst Hairer and Arieh Iserles, Numerical stability in the presence of variable coefficients , Foundations of Computational Mathematics 16 (2016) 751-777. Abstract
    2015
  • Nicola Guglielmi and Ernst Hairer, Classification of hidden dynamics in discontinuous dynamical systems , SIAM J. Appl. Dyn. Syst. 14(3) (2015) 1454-1477. Abstract
  • David Cohen, Ludwig Gauckler, Ernst Hairer, and Christian Lubich, Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions , BIT 55 (2015) 705-732 Abstract
  • Ernst Hairer and Christian Lubich, Numerical solution of ordinary differential equations , In: The Princeton Companion to Applied Mathematics, ed. N. J. Higham et. al. Princeton University Press (2015) 293-305
    2014
  • Ernst Hairer, Challenges in geometric numerical integration , In: Trends in Contemporary Mathematics. Springer INdAM Series, vol. 8 (2014), pp. 125-135 Abstract
  • Raffaele D'Ambrosio and Ernst Hairer, Long-term stability of multi-value methods for ordinary differential equations , Journal of Scientific Computing 60 (2014) 627-640 Abstract
  • Ernst Hairer and Christian Lubich, Energy-diminishing integration of gradient systems , IMA J. Numer. Anal., 34 (2014) 452-461 Abstract
  • Paola Console and Ernst Hairer, Reducing round-off errors in symmetric multistep methods , Journal of Computational and Applied Mathematics, 262 (2014) 217-222. Abstract
  • Martin J. Gander and Ernst Hairer, Analysis for parareal algorithms applied to Hamiltonian differential equations , Journal of Computational and Applied Mathematics 259 (2014) 2-13. Abstract
  • Nicola Guglielmi and Ernst Hairer, Numerical approaches for state-dependent neutral delay equations with discontinuities , Math. Comput. Simul. 95 (2014), 2-12. Abstract
  • Paola Console and Ernst Hairer, Long-term stability of symmetric partitioned linear multistep methods , In: Current challenges in stability issues for numerical differential equations. Lecture Notes in Mathematics, Vol. 2082, C.I.M.E. Foundation Subseries (2014) Abstract
    2013
  • Raffaele D'Ambrosio, Ernst Hairer, and Christophe Zbinden G-symplecticity implies conjugate-symplecticity of the underlying one-step method , BIT 53 (2013) 867-872. Abstract
  • Ernst Hairer and Christian Lubich, Long-term control of oscillations in differential equations , Internat. Math. Nachrichten 223 (2013) 1-16. Abstract
  • Ludwig Gauckler, Ernst Hairer, and Christian Lubich, Energy separation in oscillatory Hamiltonian systems without any non-resonance condition , Comm. Math. Phys. 321 (2013) 803-815. Abstract
  • Paola Console, Ernst Hairer, and Christian Lubich, Symmetric multistep methods for constrained Hamiltonian systems , Numerische Mathematik 124 (2013) 517-539. Abstract
  • Nicola Guglielmi and Ernst Hairer, Regularization of neutral delay differential equations with several delays , Journal of Dynamics and Differential Equations 25 (2013) 173-192. Abstract
  • Ernst Hairer and Christophe J. Zbinden, On conjugate-symplecticity of B-series integrators , IMA Journal of Numerical Analysis 33 (2013) 57-79. Abstract
    2012
  • Ernst Hairer and Christian Lubich, On the energy distribution in Fermi-Pasta-Ulam lattices , Arch. Ration. Mech. Anal. 205 (2012) 993-1029. Abstract
  • Ludwig Gauckler, Ernst Hairer, Christian Lubich, and Daniel Weiss, Metastable energy strata in weakly nonlinear wave equations , Comm. Partial Differential Equations 37 (2012) 1391-1413. Abstract
  • Nicola Guglielmi and Ernst Hairer, Asymptotic expansions for regularized neutral state-dependent delay equations , SIAM J. Math. Anal. 44 (2012) 2428-2458. Abstract
  • Ernst Hairer and Christian Lubich, Modulated Fourier expansions for continuous and discrete oscillatory systems , Proceeding of the FoCM'11 Conference, Budapest. Abstract
  • David Cohen and Ernst Hairer, Linear energy-preserving integrators for Poisson systems , BIT 51 (2011) 91-101. Abstract
    2011
  • Ernst Hairer and Christian Lubich, Modulated Fourier expansions for continuous and discrete oscillatory systems , Proceeding of the FoCM'11 Conference, Budapest. Abstract
  • David Cohen and Ernst Hairer, Linear energy-preserving integrators for Poisson systems , BIT 51 (2011) 91-101. Abstract
    2010
  • Ernst Hairer, Energy-preserving variant of collocation methods , JNAIAM, J. Numer. Anal. Ind. Appl. Math., 5 (2010) 73-84. Abstract
  • Philippe Chartier, Ernst Hairer and Gilles Vilmart, Algebraic structures of B-series , Foundations of Computational Mathematics 10 (2010) 407-427. Abstract
  • Ernst Hairer and Gerhard Wanner (2010), Linear multistep method, Scholarpedia, 5(4):4591.
    2009
  • Chantal Landry, Alexandre Caboussat and Ernst Hairer, Solving optimization-constrained differential equations with discontinuity points , SIAM J. Sci. Comput. 31 (2009) 3806-3826. Abstract
  • Ernst Hairer, Long-time integration of non-stiff and oscillatory Hamiltonian systems , AIP Conf. Proc. 1168 (2009) 3-6. Abstract
  • Ernst Hairer, Robert I. McLachlan and Robert D. Skeel, On energy conservation of the simplified Takahashi--Imada method , M2AN Math. Model. Numer. Anal. 43 (2009) 631-644. Abstract
  • Monique Chyba, Ernst Hairer, and Gilles Vilmart, The role of symplectic integrators in optimal control , Optim. Control Appl. Meth. 30 (2009) 367-382. Abstract
  • Ernst Hairer and Christian Lubich, Oscillations over long times in numerical Hamiltonian systems , in Highly Oscillatory Problems, edited by B. Engquist, A. Fokas, E. Hairer and A. Iserles, LMS, Lecture Notes Series 366, Cambridge University Press, 2009. Abstract
    2008
  • Ernst Hairer, Conjugate-symplecticity of linear multistep methods , J. Comp. Math. 26 (2008) 657-659. Abstract
  • David Cohen, Ernst Hairer and Christian Lubich, Conservation of energy, momentum and actions in numerical discretizations of nonlinear wave equations , Numerische Mathematik 110 (2008) 113-143. Abstract
  • Ernst Hairer and Christian Lubich, Spectral semi-discretisations of weakly nonlinear wave equations over long times , Found. Comput. Math. 8 (2008) 319-334. Abstract
  • David Cohen, Ernst Hairer and Christian Lubich, Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions , Arch. Ration. Mech. Anal. 187 (2008) 341-368. Abstract
  • Ernst Hairer, Robert I. McLachlan and Alain Razakarivony, Achieving Brouwer's law with implicit Runge-Kutta methods , BIT 48 (2008) 231-243. Abstract, Fortran code
  • Nicola Guglielmi and Ernst Hairer, Computing breaking points in implicit delay differential equations , Adv. Comput. Math. 29 (2008) 229-247. Abstract
    2007
  • Nicola Guglielmi and Ernst Hairer (2007), Stiff delay equations, Scholarpedia, 2(11):2850.
  • Ernst Hairer and Gerhard Wanner (2007), Integration numerique des equations differentielles raides , Techniques de l'ingenieur AF 653 1-15.
  • Philippe Chartier, Ernst Hairer, and Gilles Vilmart, Modified differential equations , ESAIM: Proceedings 21 (2007) 16-20. Abstract
  • Philippe Chartier, Ernst Hairer, and Gilles Vilmart, Numerical integrators based on modified differential equations , Math. of Comput. 76 (2007) 1941-1953. Abstract
  • Martin Gander and Ernst Hairer, Nonlinear Convergence Analysis for the Parareal Algorithm , Domain Decomposition Methods in Science and Engineering XVII, Lecture Notes in Computational Science and Engineering 60, Springer-Verlag, 45-56 (2007). Abstract
    2006
  • Monique Chyba, Ernst Hairer, and Gilles Vilmart, Symplectic integrators in sub-Riemannian geometry: the Martinet case , INRIA Research Report No. 6017, 2006. Abstract
  • Ernst Hairer and Gilles Vilmart, Preprocessed Discrete Moser-Veselov algorithm for the full dynamics of the rigid body , J. Phys. A: Math. Gen. 39 (2006) 13225-13235. Abstract
  • Ernst Hairer, Long-time energy conservation of numerical integrators , Foundations of Computational Mathematics, Santander 2005, London Math. Soc. Lecture Notes Ser. 331, Cambridge University Press (2006) 162-180. Abstract
  • Ernst Hairer, Symmetric linear multistep methods , BIT 46 (2006) 515-524. Abstract
    2005
  • Ernst Hairer, Important aspects of geometric numerical integration , Journal of Scientific Computing 25 (2005) 67-81. Abstract
  • Philippe Chartier, Ernst Hairer and Gilles Vilmart, A substitution law for B-series vector fields , INRIA Research Report No. 5498, 2005. Abstract
  • David Cohen, Ernst Hairer and Christian Lubich, Numerical energy conservation for multi-frequency oscillatory differential equations , BIT 45 (2005) 287-305. Abstract.
  • Ernst Hairer and Gustaf S?derlind, Explicit, time reversible, adaptive step size control , SIAM J. Sci. Comput. 26 (2005) 1838-1851. Abstract e
    2004
  • Erwan Faou, Ernst Hairer and Truong-Linh Pham, Energy conservation with non-symplectic methods: examples and counter-examples , BIT 44 (2004) 699-709. Abstract
  • Ernst Hairer and Christian Lubich, Symmetric multistep methods over long times , Numer. Math. 97 (2004) 699-723. Abstract
    2003
  • Ernst Hairer, Christian Lubich and Gerhard Wanner, Geometric numerical integration illustrated by the St?rmer-Verlet method , Acta Numerica (2003) 399-450. Abstract
  • Ernst Hairer, Global modified Hamiltonian for constrained symplectic integrators , Numer. Math. 95 (2003) 325-336. Abstract
  • David Cohen, Ernst Hairer and Christian Lubich, Modulated Fourier expansions of highly oscillatory differential equations , Foundations of Comput. Math. 3 (2003) 327-345. Abstract
    2002
  • Ernst Hairer and Martin Hairer, GniCodes - Matlab programs for geometric numerical integration , Frontiers in Numerical Analysis (Durham 2002), Springer, Berlin, 2003. Abstract
    2001
  • Ernst Hairer, Geometric integration of ordinary differential equations on manifolds , BIT 41 (2001) 996-1007. Abstract
  • Nicola Guglielmi and Ernst Hairer, Implementing Radau IIA methods for stiff delay differential equations , Computing 67, 1-12 (2001). Abstract
  • Nicola Guglielmi and Ernst Hairer, Geometric proofs of numerical stability for delay equations , IMA J. Numer. Anal. 21, 439-450 (2001). Abstract
    2000
  • Ernst Hairer and Christian Lubich, Long-time energy conservation of numerical methods for oscillatory differential equations , SIAM J. Numer. Anal. 38(2), 414-441 (2000). Abstract
  • Ernst Hairer and Gerhard Wanner, Order Stars and Stiff Integrators , J. Comput. Appl. Math. 125, 93-105 (2000), Abstract
  • Ernst Hairer and Pierre Leone, Some properties of symplectic Runge-Kutta methods , New Zealand Journal of Mathematics 29, 169-175 (2000), Abstract
  • Ernst Hairer and Constance M. Schober, Corrigendum to: "Symplectic integrators for the Ablowitz-Ladik discrete nonlinear Schroedinger equation" , Phys. Lett. A 272 (5-6), 421-422 (2000)
  • Ernst Hairer, Symmetric projection methods for differential equations on manifolds , BIT 40(4), 726-734 (2000), Abstract
  • Ernst Hairer and Christian Lubich, Energy conservation by St\"ormer-type numerical integrators. In: D.F. Griffiths, G.A. Watson (editors), Numerical Analysis 1999, CRC Press LLC, 169-190 (2000), Abstract
  • Ernst Hairer and Christian Lubich, Asymptotic expansions and backward analysis for numerical integrators . In Dynamics of Algorithms (R. de la Llave, L.R. Petzold, J. Lorenz, eds.), Springer IMA Volumes in Mathematics and its Applications, vol. 118, 91-106 (2000) Abstract
    1999
  • Ernst Hairer, Backward error analysis for multistep methods. Numer. Math. 84, 199-232 (1999), Abstract
  • Nicola Guglielmi and Ernst Hairer, Order stars and stability for delay differential equations . Numer. Math. 83, 371-383 (1999), Abstract
  • Ernst Hairer and Christian Lubich, Invariant tori of dissipatively perturbed Hamiltonian systems under symplectic discretization. Applied Numerical Mathematics 29, 57-71 (1999), Abstract
  • Stéphane Cirilli, Ernst Hairer and Benedict Leimkuhler, Asymptotic Error Analysis of the Adaptive Verlet Method . BIT 39(1), 25-33 (1999), Abstract
  • Ernst Hairer and Gerhard Wanner, Stiff differential equations solved by Radau methods . J. Comput. Appl. Math. 111(1), 93-111 (1999), Abstract
    1998
  • Ernst Hairer and Pierre Leone, Order barriers for symplectic multi-value methods , in: Numerical analysis 1997, Proceedings of the 17th Dundee Biennial Conference, June 24-27, 1997, D.F. Griffiths, D.J. Higham and G.A. Watson (editors), Pitman Research Notes in Mathematics Series vol. 380, 133-149 (1998) Abstract
    1997
  • Ernst Hairer, Variable time step integration with symplectic methods, Applied Numerical Mathematics 25, 219-227 (1997) Abstract
  • Ernst Hairer and Gerhard Wanner, Order conditions for general two-step Runge-Kutta methods , SIAM J. Numer. Anal. 34(6), 2087-2089 (1997) Abstract
  • Ernst Hairer and Christian Lubich, The lifespan of backward error analysis for numerical integrators, Numer. Math. 76, 441-462 (1997) Abstract, Erratum
  • Ernst Hairer and Daniel Stoffer, Reversible long-term integration with variable step sizes , SIAM J. Sci. Comput. 18(1), 257-269 (1997) Abstract
    1996
  • Ernst Hairer and Gerhard Wanner, On a generalization of a theorem of von Neumann , ICIAM/GAMM95 (Hamburg 1995), Z. Angew. Math. Mech. 76 (1996), suppl. 1, 95-98. Abstract
  • Ernst Hairer et Marino Zennaro, On error growth functions of Runge-Kutta methods , Applied Numerical Mathematics 22 (1996), 205-216. Abstract
    1995
  • MariPaz Calvo and Ernst Hairer, Acurate long-term integration of dynamical systems, Applied Numerical Mathematics 18 (1995), pp. 95-105. Abstract
    1994
  • Ernst Hairer, Backward analysis of numerical integrators and symplectic methods, Annals of Numerical Mathematics 1 (1994), pp. 107-132. Abstract