List of preprints
NOTE:
The list of
monographs
is on a separate page.
2024
Nicola Guglielmi and Ernst Hairer,
Applying stiff integrators for ODEs and DDES to problems
with distributed delays
,
submitted for publication
Abstract
2023
Ernst Hairer, Christian Lubich and Yanyan Shi,
Leapfrog methods for relativistic charged-particle dynamics
,
SINUM, to appear.
Abstract
Severiano González-Pinto, Ernst Hairer, and Domingo Hernández-Abreu,
PDE-convergence in Euclidean norm of AMF-W methods for multidimensional parabolic problems
,
ESAIM M2AN, to appear.
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