## Hairer, Ernst

Compute Distance To:
 Author ID: hairer.ernst Published as: Hairer, Ernst; Hairer, E. Homepage: http://www.unige.ch/~hairer/ External Links: MGP · ORCID · Wikidata · ResearchGate · dblp · GND · IdRef · theses.fr
 Documents Indexed: 152 Publications since 1973, including 16 Books 5 Contributions as Editor · 1 Further Contribution Reviewing Activity: 231 Reviews Biographic References: 1 Publication Co-Authors: 49 Co-Authors with 131 Joint Publications 1,371 Co-Co-Authors
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### Co-Authors

 26 single-authored 47 Lubich, Christian 30 Wanner, Gerhard 12 Guglielmi, Nicola 9 Nørsett, Syvert Paul 7 Iserles, Arieh 5 Gauckler, Ludwig J. 4 González-Pinto, Severiano 4 Hernandez-Abreu, Domingo 4 Vilmart, Gilles 3 Chartier, Philippe 3 Console, Paola 3 Hochbruck, Marlis 3 Roche, Michel 3 Sanz-Serna, Jesús María 2 Brasey, V. 2 Calvo, M. P. 2 D’Ambrosio, Raffaele 2 Deuflhard, Peter 2 Faou, Erwan 2 Gander, Martin Jakob 2 Leone, Pierre 2 McLachlan, Robert I. 2 Ostermann, Alexander 2 Pérez Rodríguez, S. 2 Schlichte, M. 2 Zbinden, Christophe J. 2 Zennaro, Marino 1 Beyn, Wolf-Jürgen 1 Brunner, Hermann 1 Caboussat, Alexandre 1 Cirilli, Stéphane 1 Dekker, Kees 1 Dieci, Luca 1 Engquist, Bjorn E. 1 Fokas, Athanassios S. 1 Gautschi, Walter 1 Hairer, Martin 1 Jay, Laurent-Olivier 1 Landry, Chantal 1 Leimkuhler, Benedict J. 1 Maass, Peter 1 Murua, Ander 1 Pham, Truong-Linh 1 Razakarivony, A. 1 Shi, Yanyan 1 Skeel, Robert D. 1 Söderlind, Gustaf 1 Stoffer, Daniel 1 Türke, Helmut 1 Weiss, Daniel A. 1 Zugck, J.
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### Serials

 24 Numerische Mathematik 19 BIT 9 Springer Series in Computational Mathematics 8 SIAM Journal on Numerical Analysis 7 Applied Numerical Mathematics 6 Journal of Computational and Applied Mathematics 5 IMA Journal of Numerical Analysis 5 BIT. Nordisk Tidskrift for Informationsbehandling 4 SIAM Journal on Scientific Computing 4 Foundations of Computational Mathematics 4 Undergraduate Texts in Mathematics 3 Computing 3 Oberwolfach Reports 2 Archive for Rational Mechanics and Analysis 2 Mathematics of Computation 2 Journal of Scientific Computing 2 Numerical Algorithms 2 Communications in Partial Differential Equations 2 SIAM Journal on Mathematical Analysis 2 Lecture Notes in Mathematics 1 Communications in Mathematical Physics 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Mathematics and Computers in Simulation 1 SIAM Journal on Scientific and Statistical Computing 1 Journal of Computational Mathematics 1 Internationale Mathematische Nachrichten 1 Journal of Physics A: Mathematical and General 1 Journal of Dynamics and Differential Equations 1 New Zealand Journal of Mathematics 1 Annals of Numerical Mathematics 1 Advances in Computational Mathematics 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Nonlinear Dynamics 1 Journal of Inequalities and Applications 1 SIAM Journal on Applied Dynamical Systems 1 Acta Numerica 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 London Mathematical Society Lecture Note Series 1 JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics 1 SMAI Journal of Computational Mathematics 1 Springer-Lehrbuch
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### Fields

 142 Numerical analysis (65-XX) 73 Ordinary differential equations (34-XX) 44 Dynamical systems and ergodic theory (37-XX) 17 Mechanics of particles and systems (70-XX) 9 Partial differential equations (35-XX) 7 Integral equations (45-XX) 6 History and biography (01-XX) 6 Real functions (26-XX) 5 General and overarching topics; collections (00-XX) 5 Optics, electromagnetic theory (78-XX) 4 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Statistics (62-XX) 1 Fluid mechanics (76-XX) 1 Quantum theory (81-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

### Citations contained in zbMATH Open

144 Publications have been cited 8,266 times in 5,558 Documents Cited by Year
Solving ordinary differential equations. I: Nonstiff problems. 2. rev. ed. Zbl 0789.65048
Hairer, Ernst; Nørsett, Syvert P.; Wanner, Gerhard
1993
Solving ordinary differential equations. II: Stiff and differential-algebraic problems. 2nd rev. ed. Zbl 0859.65067
Hairer, Ernst; Wanner, Gerhard
1996
Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. 2nd ed. Zbl 1094.65125
Hairer, Ernst; Lubich, Christian; Wanner, Gerhard
2006
Solving ordinary differential equations II: Stiff and differential-algebraic problems. Zbl 0729.65051
Hairer, Ernst; Wanner, Gerhard
1991
Solving ordinary differential equations. I: Nonstiff problems. Zbl 0638.65058
Hairer, Ernst; Nørsett, Syvert P.; Wanner, Gerhard
1987
Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. Zbl 0994.65135
Hairer, Ernst; Lubich, Christian; Wanner, Gerhard
2002
Solving ordinary differential equations. II: Stiff and differential-algebraic problems. Reprint of the 1996 2nd revised ed. Zbl 1192.65097
Hairer, Ernst; Wanner, Gerhard
2010
The numerical solution of differential-algebraic systems by Runge-Kutta methods. Zbl 0683.65050
Hairer, Ernst; Lubich, Christian; Roche, Michel
1989
Solving ordinary differential equations. I: Nonstiff problems. 2nd revised ed., 3rd corrected printing. Zbl 1185.65115
Hairer, Ernst; Nørsett, Syvert P.; Wanner, Gerhard
2010
Order stars and stability theorems. Zbl 0444.65039
Wanner, Gerhard; Hairer, Ernst; Nørsett, Syvert P.
1978
Long-time energy conservation of numerical methods for oscillatory differential equations. Zbl 0988.65118
Hairer, Ernst; Lubich, Christian
2000
Energy-preserving variant of collocation methods. Zbl 1432.65185
Hairer, E.
2010
Geometric numerical integration illustrated by the Störmer-Verlet method. Zbl 1046.65110
Hairer, Ernst; Lubich, Christian; Wanner, Gerhard
2003
Unconditionally stable methods for second order differential equations. Zbl 0393.65035
Hairer, E.
1979
On the Butcher group and general multi-value methods. Zbl 0293.65050
Hairer, Ernst; Wanner, Gerhard
1974
Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations. Zbl 0657.65093
Hairer, E.; Lubich, Ch.; Roche, M.
1988
Fast numerical solution of nonlinear Volterra convolution equations. Zbl 0581.65095
Hairer, E.; Lubich, Ch.; Schlichte, M.
1985
A theory for Nyström methods. Zbl 0307.65053
Hairer, Ernst; Wanner, Gerhard
1976
Linear energy-preserving integrators for Poisson systems. Zbl 1216.65175
Cohen, David; Hairer, Ernst
2011
One-step and extrapolation methods for differential-algebraic systems. Zbl 0635.65083
Deuflhard, P.; Hairer, E.; Zugck, J.
1987
Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations. Zbl 1163.65066
Cohen, David; Hairer, Ernst; Lubich, Christian
2008
The life-span of backward error analysis for numerical integrators. Zbl 0874.65061
Hairer, E.; Lubich, Ch.
1997
Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. Reprint of the second 2006 ed. Zbl 1228.65237
Hairer, Ernst; Lubich, Christian; Wanner, Gerhard
2010
Nonlinear convergence analysis for the parareal algorithm. Zbl 1140.65336
Gander, Martin J.; Hairer, Ernst
2008
Backward analysis of numerical integrators and symplectic methods. Zbl 0828.65097
Hairer, Ernst
1994
Stiff differential equations solved by Radau methods. Zbl 0945.65080
Hairer, Ernst; Wanner, Gerhard
1999
Implementing Radau IIA methods for stiff delay differential equations. Zbl 0986.65069
Guglielmi, N.; Hairer, E.
2001
Algebraically stable and implementable Runge-Kutta methods of high order. Zbl 0533.65041
Hairer, Ernst; Wanner, Gerhard
1981
Algebraic structures of B-series. Zbl 1201.65124
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
2010
On the stability of semi-implicit methods for ordinary differential equations. Zbl 0489.65046
Hairer, E.; Bader, G.; Lubich, Ch.
1982
Multistep-multistage-multiderivative methods for ordinary differential equations. Zbl 0271.65048
Hairer, Ernst; Wanner, Gerhard
1973
Runge-Kutta theory for Volterra integral equations of the second kind. Zbl 0496.65066
Brunner, Hermann; Hairer, Ernst; Nørsett, Syvert P.
1982
Error of Rosenbrock methods for stiff problems studied via differential algebraic equations. Zbl 0674.65039
Hairer, E.; Lubich, Ch.; Roche, M.
1989
Computing breaking points in implicit delay differential equations. Zbl 1160.65041
Guglielmi, Nicola; Hairer, Ernst
2008
Méthodes de Nystrom pour l’équation différentielle y”=f(x,y). Zbl 0325.65033
Hairer, Ernst
1977
Order conditions for numerical methods for partitioned ordinary differential equations. Zbl 0462.65049
Hairer, E.
1981
Variable time step integration with symplectic methods. Zbl 0884.65073
Hairer, E.
1997
Numerical energy conservation for multi-frequency oscillatory differential equations. Zbl 1083.65117
Cohen, D.; Hairer, E.; Lubich, Ch.
2005
Half-explicit Runge-Kutta methods for differential-algebraic systems of index 2. Zbl 0785.65082
Brasey, V.; Hairer, E.
1993
Energy conservation with non-symplectic methods: examples and counter-examples. Zbl 1082.65132
Faou, Erwan; Hairer, Ernst; Pham, Truong-Linh
2004
A one-step method of order 10 for y”=f(x,y). Zbl 0482.65042
Hairer, E.
1982
Energy-diminishing integration of gradient systems. Zbl 1321.65115
Hairer, Ernst; Lubich, Christian
2014
Fast numerical solution of weakly singular Volterra integral equations. Zbl 0654.65091
Hairer, E.; Lubich, Ch.; Schlichte, M.
1988
Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions. Zbl 1145.35087
Cohen, David; Hairer, Ernst; Lubich, Christian
2008
Unconditionally stable explicit methods for parabolic equations. Zbl 0454.65052
Hairer, E.
1980
Order of convergence of one-step methods for Volterra integral equations of the second kind. Zbl 0519.65088
Hairer, Ernst; Lubich, Ch.; Nørsett, Syvert P.
1983
Asymptotic expansions of the global error of fixed-stepsize methods. Zbl 0571.65066
Hairer, E.; Lubich, C.
1984
Order stars and stability for delay differential equations. Zbl 0937.65079
Guglielmi, Nicola; Hairer, Ernst
1999
Symmetric multistep methods over long times. Zbl 1060.65074
Hairer, Ernst; Lubich, Christian
2004
GniCodes –Matlab programs for geometric numerical integration. Zbl 1028.65136
Hairer, Ernst; Hairer, Martin
2003
Modulated Fourier expansions of highly oscillatory differential equations. Zbl 1056.34005
Cohen, David; Hairer, Ernst; Lubich, Christian
2003
Symmetric projection methods for differential equations on manifolds. Zbl 0968.65108
Hairer, E.
2000
Order conditions for general two-step Runge-Kutta methods. Zbl 0890.65077
Hairer, Ernst; Wanner, Gerhard
1997
Analysis for parareal algorithms applied to Hamiltonian differential equations. Zbl 1291.65209
Gander, Martin J.; Hairer, Ernst
2014
Achieving Brouwer’s law with implicit Runge-Kutta methods. Zbl 1148.65058
Hairer, E.; McLachlan, R. I.; Razakarivony, A.
2008
Spectral semi-discretisations of weakly non-linear wave equations over long times. Zbl 1156.35007
Hairer, E.; Lubich, C.
2008
Accurate long-term integration of dynamical systems. Zbl 0837.65071
Calvo, M. P.; Hairer, E.
1995
Highly oscillatory problems. Zbl 1170.37002
2009
Explicit, time reversible, adaptive step size control. Zbl 1081.65117
Hairer, Ernst; Söderlind, Gustaf
2005
Classification of hidden dynamics in discontinuous dynamical systems. Zbl 1329.34028
Guglielmi, Nicola; Hairer, Ernst
2015
Analysis by its history. Zbl 0842.26002
Hairer, E.; Wanner, G.
1995
Geometric proofs of numerical stability for delay equations. Zbl 0976.65077
Guglielmi, Nicola; Hairer, Ernst
2001
On conjugate symplecticity of B-series integrators. Zbl 1329.65307
Hairer, Ernst; Zbinden, Christophe J.
2013
Numerical integrators based on modified differential equations. Zbl 1122.65059
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
2007
Energy behaviour of the Boris method for charged-particle dynamics. Zbl 1404.65309
Hairer, Ernst; Lubich, Christian
2018
Long-term analysis of the Störmer-Verlet method for Hamiltonian systems with a solution-dependent high frequency. Zbl 1408.65100
Hairer, Ernst; Lubich, Christian
2016
Long-term stability of multi-value methods for ordinary differential equations. Zbl 1312.65111
D’Ambrosio, R.; Hairer, E.
2014
Symmetric multistep methods for charged-particle dynamics. Zbl 1416.78037
Hairer, Ernst; Lubich, Christian
2017
Equilibria of Runge-Kutta methods. Zbl 0693.65047
Hairer, E.; Iserles, A.; Sanz-Serna, J. M.
1990
Highest possible order of algebraically stable diagonally implicit Runge- Kutta methods. Zbl 0425.65037
Hairer, E.
1980
G-symplecticity implies conjugate-symplecticity of the underlying one-step method. Zbl 1282.65168
D’Ambrosio, R.; Hairer, E.; Zbinden, C. J.
2013
A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field. Zbl 1434.65312
Hairer, Ernst; Lubich, Christian; Wang, Bin
2020
Backward error analysis for multistep methods. Zbl 0941.65077
Hairer, Ernst
1999
Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions. Zbl 1331.65171
Cohen, David; Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian
2015
On the stability of Volterra-Runge-Kutta methods. Zbl 0532.65086
Hairer, E.; Lubich, Ch.
1984
Reversible long-term integration with variable stepsizes. Zbl 0871.65075
Hairer, Ernst; Stoffer, Daniel
1997
Extrapolation at stiff differential equations. Zbl 0643.65034
Hairer, E.; Lubich, C.
1988
On the energy distribution in Fermi-Pasta-Ulam lattices. Zbl 1283.70011
Hairer, Ernst; Lubich, Christian
2012
On energy conservation of the simplified Takahashi-Imada method. Zbl 1172.65067
Hairer, Ernst; McLachlan, Robert I.; Skeel, Robert D.
2009
AMF-type W-methods for parabolic problems with mixed derivatives. Zbl 1397.65159
González-Pinto, S.; Hairer, E.; Hernández-Abreu, D.; Pérez-Rodríguez, S.
2018
Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field. Zbl 1432.78013
Hairer, Ernst; Lubich, Christian
2020
The non-existence of symplectic multi-derivative Runge-Kutta methods. Zbl 0816.65043
Hairer, E.; Murua, A.; Sanz-Serna, J. M.
1994
The equivalence of B-stability and A-stability. Zbl 0571.65060
Hairer, E.; Türke, H.
1984
Energy separation in oscillatory Hamiltonian systems without any non-resonance condition. Zbl 1329.70045
Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian
2013
Oscillation over long times in numerical Hamiltonian systems. Zbl 1180.37121
Hairer, Ernst; Lubich, Christian
2009
Numerical methods for singular nonlinear integrodifferential equations. Zbl 0631.65142
Hairer, E.; Maass, P.
1987
Conjugate-symplecticity of linear multistep methods. Zbl 1174.65055
Hairer, Ernst
2008
Preprocessed discrete Moser-Veselov algorithm for the full dynamics of a rigid body. Zbl 1127.70002
Hairer, Ernst; Vilmart, Gilles
2006
Energy conservation by Störmer-type numerical integrators. Zbl 0952.65053
Hairer, E.; Lubich, Ch.
2000
Implicit Runge-Kutta methods for higher index differential-algebraic systems. Zbl 0834.65062
Hairer, E.; Jay, L.
1993
On error growth functions of Runge-Kutta methods. Zbl 0871.65071
Hairer, E.; Zennaro, M.
1996
A necessary condition for BSI-stability. Zbl 0579.65091
Dekker, Kees; Hairer, Ernst
1985
Solving optimization-constrained differential equations with discontinuity points, with application to atmospheric chemistry. Zbl 1391.86007
Landry, Chantal; Caboussat, Alexandre; Hairer, Ernst
2009
Asymptotic expansions for regularized state-dependent neutral delay equations. Zbl 1257.34060
Guglielmi, Nicola; Hairer, Ernst
2012
Order barriers for symplectic multi-value methods. Zbl 0902.65027
Hairer, E.; Leone, P.
1998
Symmetric linear multistep. Zbl 1149.65054
Hairer, Ernst
2006
Asymptotic expansions and backward analysis for numerical integrators. Zbl 0942.65092
Hairer, Ernst; Lubich, Christian
2000
On the order of iterated defect correction. An algebraic proof. Zbl 0414.65045
Hairer, E.
1978
Metastable energy strata in weakly nonlinear wave equations. Zbl 1255.35042
Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian; Weiss, Daniel
2012
Invariant tori of dissipatively perturbed Hamiltonian systems under symplectic discretization. Zbl 1022.37042
Hairer, Ernst; Lubich, Christian
1999
Power boundedness in the maximum norm of stability matrices for ADI methods. Zbl 07381114
González-Pinto, S.; Hairer, E.; Hernández-Abreu, D.
2021
A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field. Zbl 1434.65312
Hairer, Ernst; Lubich, Christian; Wang, Bin
2020
Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field. Zbl 1432.78013
Hairer, Ernst; Lubich, Christian
2020
Convergence in $$\ell_2$$ and $$\ell_\infty$$ norm of one-stage AMF-W-methods for parabolic problems. Zbl 1436.65129
González-Pinto, S.; Hairer, E.; Hernandez-Abreu, Domingo
2020
Energy behaviour of the Boris method for charged-particle dynamics. Zbl 1404.65309
Hairer, Ernst; Lubich, Christian
2018
AMF-type W-methods for parabolic problems with mixed derivatives. Zbl 1397.65159
González-Pinto, S.; Hairer, E.; Hernández-Abreu, D.; Pérez-Rodríguez, S.
2018
PDE-W-methods for parabolic problems with mixed derivatives. Zbl 1447.65060
González-Pinto, S.; Hairer, E.; Hernández-Abreu, D.; Pérez-Rodríguez, S.
2018
Dynamics, numerical analysis, and some geometry. Zbl 1451.62056
Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian
2018
Symmetric multistep methods for charged-particle dynamics. Zbl 1416.78037
Hairer, Ernst; Lubich, Christian
2017
Solutions leaving a codimension-$$2$$ sliding. Zbl 1375.34025
Guglielmi, Nicola; Hairer, Ernst
2017
Banded, stable, skew-symmetric differentiation matrices of high order. Zbl 1433.65138
Hairer, Ernst; Iserles, Arieh
2017
Long-term analysis of the Störmer-Verlet method for Hamiltonian systems with a solution-dependent high frequency. Zbl 1408.65100
Hairer, Ernst; Lubich, Christian
2016
Numerical stability in the presence of variable coefficients. Zbl 1347.65144
Hairer, Ernst; Iserles, Arieh
2016
Long-term analysis of semilinear wave equations with slowly varying wave speed. Zbl 1368.35164
Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian
2016
Path-regularization of linear neutral delay differential equations with several delays. Zbl 1343.34153
Guglielmi, Nicola; Hairer, Ernst
2016
Classification of hidden dynamics in discontinuous dynamical systems. Zbl 1329.34028
Guglielmi, Nicola; Hairer, Ernst
2015
Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions. Zbl 1331.65171
Cohen, David; Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian
2015
Energy-diminishing integration of gradient systems. Zbl 1321.65115
Hairer, Ernst; Lubich, Christian
2014
Analysis for parareal algorithms applied to Hamiltonian differential equations. Zbl 1291.65209
Gander, Martin J.; Hairer, Ernst
2014
Long-term stability of multi-value methods for ordinary differential equations. Zbl 1312.65111
D&rsquo;Ambrosio, R.; Hairer, E.
2014
Long-term stability of symmetric partitioned linear multistep methods. Zbl 1318.65078
Console, Paola; Hairer, Ernst
2014
Challenges in geometric numerical integration. Zbl 1325.65174
Hairer, Ernst
2014
On conjugate symplecticity of B-series integrators. Zbl 1329.65307
Hairer, Ernst; Zbinden, Christophe J.
2013
G-symplecticity implies conjugate-symplecticity of the underlying one-step method. Zbl 1282.65168
D&rsquo;Ambrosio, R.; Hairer, E.; Zbinden, C. J.
2013
Energy separation in oscillatory Hamiltonian systems without any non-resonance condition. Zbl 1329.70045
Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian
2013
Modulated Fourier expansions for continuous and discrete oscillatory systems. Zbl 1316.42005
Hairer, Ernst; Lubich, Christian
2013
Symmetric multistep methods for constrained Hamiltonian systems. Zbl 1290.65125
Console, Paola; Hairer, Ernst; Lubich, Christian
2013
Long-term control of oscillations in differential equations. Zbl 1338.65182
Hairer, Ernst; Lubich, Christian
2013
Regularization of neutral delay differential equations with several delays. Zbl 1283.34074
Guglielmi, Nicola; Hairer, Ernst
2013
On the energy distribution in Fermi-Pasta-Ulam lattices. Zbl 1283.70011
Hairer, Ernst; Lubich, Christian
2012
Asymptotic expansions for regularized state-dependent neutral delay equations. Zbl 1257.34060
Guglielmi, Nicola; Hairer, Ernst
2012
Metastable energy strata in weakly nonlinear wave equations. Zbl 1255.35042
Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian; Weiss, Daniel
2012
Linear energy-preserving integrators for Poisson systems. Zbl 1216.65175
Cohen, David; Hairer, Ernst
2011
Solving ordinary differential equations. II: Stiff and differential-algebraic problems. Reprint of the 1996 2nd revised ed. Zbl 1192.65097
Hairer, Ernst; Wanner, Gerhard
2010
Solving ordinary differential equations. I: Nonstiff problems. 2nd revised ed., 3rd corrected printing. Zbl 1185.65115
Hairer, Ernst; Nørsett, Syvert P.; Wanner, Gerhard
2010
Energy-preserving variant of collocation methods. Zbl 1432.65185
Hairer, E.
2010
Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. Reprint of the second 2006 ed. Zbl 1228.65237
Hairer, Ernst; Lubich, Christian; Wanner, Gerhard
2010
Algebraic structures of B-series. Zbl 1201.65124
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
2010
Highly oscillatory problems. Zbl 1170.37002
2009
On energy conservation of the simplified Takahashi-Imada method. Zbl 1172.65067
Hairer, Ernst; McLachlan, Robert I.; Skeel, Robert D.
2009
Oscillation over long times in numerical Hamiltonian systems. Zbl 1180.37121
Hairer, Ernst; Lubich, Christian
2009
Solving optimization-constrained differential equations with discontinuity points, with application to atmospheric chemistry. Zbl 1391.86007
Landry, Chantal; Caboussat, Alexandre; Hairer, Ernst
2009
Long-time integration of non-stiff and oscillatory Hamiltonian systems. Zbl 1183.65169
Hairer, Ernst
2009
Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations. Zbl 1163.65066
Cohen, David; Hairer, Ernst; Lubich, Christian
2008
Nonlinear convergence analysis for the parareal algorithm. Zbl 1140.65336
Gander, Martin J.; Hairer, Ernst
2008
Computing breaking points in implicit delay differential equations. Zbl 1160.65041
Guglielmi, Nicola; Hairer, Ernst
2008
Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions. Zbl 1145.35087
Cohen, David; Hairer, Ernst; Lubich, Christian
2008
Achieving Brouwer’s law with implicit Runge-Kutta methods. Zbl 1148.65058
Hairer, E.; McLachlan, R. I.; Razakarivony, A.
2008
Spectral semi-discretisations of weakly non-linear wave equations over long times. Zbl 1156.35007
Hairer, E.; Lubich, C.
2008
Conjugate-symplecticity of linear multistep methods. Zbl 1174.65055
Hairer, Ernst
2008
Analysis by its history. Corr. 4th printing. Zbl 1139.26001
Hairer, Ernst; Wanner, Gerhard
2008
Numerical integrators based on modified differential equations. Zbl 1122.65059
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
2007
Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. 2nd ed. Zbl 1094.65125
Hairer, Ernst; Lubich, Christian; Wanner, Gerhard
2006
Preprocessed discrete Moser-Veselov algorithm for the full dynamics of a rigid body. Zbl 1127.70002
Hairer, Ernst; Vilmart, Gilles
2006
Symmetric linear multistep. Zbl 1149.65054
Hairer, Ernst
2006
Long-time energy conservation of numerical integrators. Zbl 1106.65334
Hairer, Ernst
2006
Report 14/2006: Geometric Numerical Integration (March 19th – March 25th, 2006). Zbl 1109.65301
2006
Numerical energy conservation for multi-frequency oscillatory differential equations. Zbl 1083.65117
Cohen, D.; Hairer, E.; Lubich, Ch.
2005
Explicit, time reversible, adaptive step size control. Zbl 1081.65117
Hairer, Ernst; Söderlind, Gustaf
2005
Important aspects of geometric numerical integration. Zbl 1203.65115
Hairer, Ernst
2005
Energy conservation with non-symplectic methods: examples and counter-examples. Zbl 1082.65132
Faou, Erwan; Hairer, Ernst; Pham, Truong-Linh
2004
Symmetric multistep methods over long times. Zbl 1060.65074
Hairer, Ernst; Lubich, Christian
2004
Geometric numerical integration illustrated by the Störmer-Verlet method. Zbl 1046.65110
Hairer, Ernst; Lubich, Christian; Wanner, Gerhard
2003
GniCodes –Matlab programs for geometric numerical integration. Zbl 1028.65136
Hairer, Ernst; Hairer, Martin
2003
Modulated Fourier expansions of highly oscillatory differential equations. Zbl 1056.34005
Cohen, David; Hairer, Ernst; Lubich, Christian
2003
Global modified Hamiltonian for constrained symplectic integrators. Zbl 1041.65102
Hairer, Ernst
2003
Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. Zbl 0994.65135
Hairer, Ernst; Lubich, Christian; Wanner, Gerhard
2002
Implementing Radau IIA methods for stiff delay differential equations. Zbl 0986.65069
Guglielmi, N.; Hairer, E.
2001
Geometric proofs of numerical stability for delay equations. Zbl 0976.65077
Guglielmi, Nicola; Hairer, Ernst
2001
Long-time energy conservation of numerical methods for oscillatory differential equations. Zbl 0988.65118
Hairer, Ernst; Lubich, Christian
2000
Symmetric projection methods for differential equations on manifolds. Zbl 0968.65108
Hairer, E.
2000
Energy conservation by Störmer-type numerical integrators. Zbl 0952.65053
Hairer, E.; Lubich, Ch.
2000
Asymptotic expansions and backward analysis for numerical integrators. Zbl 0942.65092
Hairer, Ernst; Lubich, Christian
2000
Order stars and stiff integrators. Zbl 0988.65059
Hairer, Ernst; Wanner, Gerhard
2000
Analysis by its history. Corr. 3rd printing. Zbl 0964.26002
Hairer, Ernst; Wanner, Gerhard
2000
Stiff differential equations solved by Radau methods. Zbl 0945.65080
Hairer, Ernst; Wanner, Gerhard
1999
Order stars and stability for delay differential equations. Zbl 0937.65079
Guglielmi, Nicola; Hairer, Ernst
1999
Backward error analysis for multistep methods. Zbl 0941.65077
Hairer, Ernst
1999
Invariant tori of dissipatively perturbed Hamiltonian systems under symplectic discretization. Zbl 1022.37042
Hairer, Ernst; Lubich, Christian
1999
Asymptotic error analysis of the adaptive Verlet method. Zbl 0924.65070
Cirilli, Stéphane; Hairer, Ernst; Leimkuhler, Benedict
1999
Order barriers for symplectic multi-value methods. Zbl 0902.65027
Hairer, E.; Leone, P.
1998
The life-span of backward error analysis for numerical integrators. Zbl 0874.65061
Hairer, E.; Lubich, Ch.
1997
Variable time step integration with symplectic methods. Zbl 0884.65073
Hairer, E.
1997
Order conditions for general two-step Runge-Kutta methods. Zbl 0890.65077
Hairer, Ernst; Wanner, Gerhard
1997
Reversible long-term integration with variable stepsizes. Zbl 0871.65075
Hairer, Ernst; Stoffer, Daniel
1997
Solving ordinary differential equations. II: Stiff and differential-algebraic problems. 2nd rev. ed. Zbl 0859.65067
Hairer, Ernst; Wanner, Gerhard
1996
On error growth functions of Runge-Kutta methods. Zbl 0871.65071
Hairer, E.; Zennaro, M.
1996
On a generalization of a theorem of von Neumann. Zbl 0900.65238
Hairer, E.; Wanner, G.
1996
Accurate long-term integration of dynamical systems. Zbl 0837.65071
Calvo, M. P.; Hairer, E.
1995
Analysis by its history. Zbl 0842.26002
Hairer, E.; Wanner, G.
1995
Further reduction in the number of independent order conditions for symplectic, explicit partitioned Runge-Kutta and Runge-Kutta-Nyström methods. Zbl 0885.65087
Calvo, M. P.; Hairer, E.
1995
Backward analysis of numerical integrators and symplectic methods. Zbl 0828.65097
Hairer, Ernst
1994
The non-existence of symplectic multi-derivative Runge-Kutta methods. Zbl 0816.65043
Hairer, E.; Murua, A.; Sanz-Serna, J. M.
1994
Symplectic Runge-Kutta methods with real eigenvalues. Zbl 0807.65081
Hairer, E.; Wanner, G.
1994
Solving ordinary differential equations. I: Nonstiff problems. 2. rev. ed. Zbl 0789.65048
Hairer, Ernst; Nørsett, Syvert P.; Wanner, Gerhard
1993
Half-explicit Runge-Kutta methods for differential-algebraic systems of index 2. Zbl 0785.65082
Brasey, V.; Hairer, E.
1993
Implicit Runge-Kutta methods for higher index differential-algebraic systems. Zbl 0834.65062
Hairer, E.; Jay, L.
1993
Symmetrized half-explicit methods for constrained mechanical systems. Zbl 0787.65043
Brasey, V.; Hairer, E.
1993
Dense output for the GBS extrapolation method. Zbl 0810.65074
Hairer, E.; Ostermann, A.
1992
Solving ordinary differential equations II: Stiff and differential-algebraic problems. Zbl 0729.65051
Hairer, Ernst; Wanner, Gerhard
1991
...and 44 more Documents
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### Cited by 5,879 Authors

 80 Wu, Xinyuan 74 Hairer, Ernst 73 Lubich, Christian 62 Jackiewicz, Zdzislaw 60 Weiner, Rüdiger 42 Wang, Yushun 41 Butcher, John C. 41 Ostermann, Alexander 41 Simos, Theodore E. 39 Wang, Bin 35 Chartier, Philippe 35 You, Xiong 34 Brugnano, Luigi 33 Ramos, Higinio 33 Sandu, Adrian 31 Abdi, Ali 31 Montijano, Juan Ignacio 31 Murua, Ander 30 Sanz-Serna, Jesús María 28 Auzinger, Winfried 28 D’Ambrosio, Raffaele 28 Fang, Yonglei 28 González-Pinto, Severiano 28 van der Houwen, Pieter J. 28 Xiao, Aiguo 27 Hojjati, Gholamreza 27 Rández, Luis 26 Casas, Fernando 26 Iserles, Arieh 26 Kulikov, Gennady Yur’evich 26 Van Daele, Marnix 25 Blanes, Sergio 25 Calvo, Manuel 25 Faou, Erwan 25 Hundsdorfer, Willem H. 24 Burrage, Kevin 24 McLachlan, Robert I. 24 Sommeijer, Ben P. 24 Vanden Berghe, Guido 23 Franco, J. Méndez 23 Iavernaro, Felice 23 Owren, Brynjulf 23 Shi, Wei 23 Tsitouras, Charalampos 23 Zhang, Chengjian 22 Celledoni, Elena 22 Li, Jiyong 22 Paternoster, Beatrice 22 Podhaisky, Helmut 22 Schmitt, Bernhard A. 22 Vigo-Aguiar, Jesus 21 Cong, Nguyen Huu 21 Gan, Siqing 20 Arnold, Martin 20 Huang, Chengming 20 Shampine, Lawrence Fred 20 Sun, Yajuan 20 Verwer, Jan G. 20 Vilmart, Gilles 19 Hernandez-Abreu, Domingo 19 Hong, Jialin 19 Leok, Melvin 19 Li, Shoufu 19 Martín de Diego, David 19 Mehrmann, Volker 19 Strehmel, Karl 19 Wang, Wansheng 19 Wanner, Gerhard 18 Higueras, Inmaculada 18 Izzo, Giuseppe 18 Jator, Samuel N. 18 Jiang, Yaolin 18 Schratz, Katharina 18 Simeon, Bernd 18 Tian, Hongjiong 17 Akrivis, Georgios D. 17 Cai, Wenjun 17 Guglielmi, Nicola 17 Hartmann, Stefan 17 Spijker, Marc N. 17 Zhao, Jingjun 16 Conte, Dajana 16 Gong, Yuezheng 16 Günther, Michael 16 Higham, Desmond J. 16 Ismail, Fudziah Bt. 16 Karasözen, Bülent 16 Ketcheson, David I. 16 Nørsett, Syvert Paul 16 Rogov, Boris V. 16 Russo, Giovanni 16 Söderlind, Gustaf 16 Tang, Yifa 15 Boscarino, Sebastiano 15 De Meyer, Hans E. 15 Gander, Martin Jakob 15 Koch, Othmar 15 Liu, Kai 15 Martín-Vaquero, Jesús 15 Rößler, Andreas ...and 5,779 more Authors
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### Cited in 493 Serials

 512 Journal of Computational and Applied Mathematics 494 Applied Numerical Mathematics 319 Journal of Computational Physics 266 BIT 232 Applied Mathematics and Computation 167 Numerical Algorithms 162 Numerische Mathematik 156 Journal of Scientific Computing 142 Computers & Mathematics with Applications 113 Computer Methods in Applied Mechanics and Engineering 111 SIAM Journal on Scientific Computing 105 International Journal of Computer Mathematics 100 Mathematics of Computation 81 SIAM Journal on Numerical Analysis 64 Mathematics and Computers in Simulation 62 Computer Physics Communications 55 International Journal for Numerical Methods in Engineering 52 Foundations of Computational Mathematics 50 Computing 47 Applied Mathematics Letters 47 Multibody System Dynamics 38 Celestial Mechanics and Dynamical Astronomy 38 Communications in Nonlinear Science and Numerical Simulation 37 Physica D 35 Advances in Computational Mathematics 34 Computational and Applied Mathematics 32 Computers and Fluids 31 Journal of Mathematical Chemistry 30 Physics Letters. A 28 Calcolo 28 Computational Mathematics and Mathematical Physics 27 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 26 Computational Mechanics 25 Mathematical and Computer Modelling 24 Discrete and Continuous Dynamical Systems 23 Numerical Methods for Partial Differential Equations 23 Japan Journal of Industrial and Applied Mathematics 23 Mathematical Problems in Engineering 22 Nonlinear Dynamics 21 Applied Mathematical Modelling 21 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 19 Linear Algebra and its Applications 19 Discrete and Continuous Dynamical Systems. Series B 19 Advances in Difference Equations 19 Communications in Computational Physics 18 Journal of Nonlinear Science 17 Journal of Mathematical Analysis and Applications 16 Journal of Applied Mathematics and Computing 16 Multiscale Modeling & Simulation 16 Journal of Computational Dynamics 15 Chaos, Solitons and Fractals 15 Doklady Mathematics 15 Abstract and Applied Analysis 15 Journal of Applied Mathematics 15 Discrete and Continuous Dynamical Systems. Series S 14 Combustion Theory and Modelling 13 Journal of Optimization Theory and Applications 13 Optimization Methods & Software 13 Regular and Chaotic Dynamics 13 International Journal of Modern Physics C 13 Differential Equations 13 BIT. Nordisk Tidskrift for Informationsbehandling 13 International Journal of Applied and Computational Mathematics 12 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 12 Journal of Mathematical Sciences (New York) 12 Journal of Difference Equations and Applications 11 Mathematical Biosciences 11 Journal of Differential Equations 11 SIAM Journal on Control and Optimization 11 Numerical Linear Algebra with Applications 11 Matematicheskoe Modelirovanie 11 Advances in Applied Mathematics and Mechanics 10 International Journal for Numerical Methods in Fluids 10 Journal of Mathematical Physics 10 Applied Mathematics and Mechanics. (English Edition) 10 SIAM Journal on Matrix Analysis and Applications 10 Journal of Dynamics and Differential Equations 10 Chaos 9 Journal of Fluid Mechanics 9 Mathematical Methods in the Applied Sciences 9 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 9 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 9 Numerical Functional Analysis and Optimization 9 Communications in Numerical Methods in Engineering 9 Computing and Visualization in Science 8 Bulletin of Mathematical Biology 8 Automatica 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Systems & Control Letters 8 Mathematical and Computer Modelling of Dynamical Systems 8 SIAM Journal on Applied Dynamical Systems 8 Mediterranean Journal of Mathematics 8 Acta Numerica 8 Journal of Geometric Mechanics 8 Afrika Matematika 8 Statistics and Computing 8 Journal of Theoretical Biology 8 Communications on Applied Mathematics and Computation 7 Nonlinearity 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik ...and 393 more Serials
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### Cited in 60 Fields

 4,364 Numerical analysis (65-XX) 1,743 Ordinary differential equations (34-XX) 1,039 Partial differential equations (35-XX) 594 Dynamical systems and ergodic theory (37-XX) 476 Mechanics of particles and systems (70-XX) 468 Fluid mechanics (76-XX) 263 Probability theory and stochastic processes (60-XX) 243 Mechanics of deformable solids (74-XX) 223 Biology and other natural sciences (92-XX) 165 Systems theory; control (93-XX) 152 Integral equations (45-XX) 135 Statistical mechanics, structure of matter (82-XX) 134 Calculus of variations and optimal control; optimization (49-XX) 118 Quantum theory (81-XX) 104 Optics, electromagnetic theory (78-XX) 101 Computer science (68-XX) 89 Classical thermodynamics, heat transfer (80-XX) 81 Operations research, mathematical programming (90-XX) 64 Linear and multilinear algebra; matrix theory (15-XX) 61 Operator theory (47-XX) 56 Statistics (62-XX) 53 Approximations and expansions (41-XX) 52 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 51 Differential geometry (53-XX) 51 Information and communication theory, circuits (94-XX) 45 Geophysics (86-XX) 40 Real functions (26-XX) 35 Difference and functional equations (39-XX) 34 Combinatorics (05-XX) 25 Associative rings and algebras (16-XX) 23 Relativity and gravitational theory (83-XX) 22 Nonassociative rings and algebras (17-XX) 22 Global analysis, analysis on manifolds (58-XX) 22 Astronomy and astrophysics (85-XX) 18 History and biography (01-XX) 18 Integral transforms, operational calculus (44-XX) 15 Topological groups, Lie groups (22-XX) 15 Functional analysis (46-XX) 12 General and overarching topics; collections (00-XX) 12 Harmonic analysis on Euclidean spaces (42-XX) 10 Special functions (33-XX) 6 Geometry (51-XX) 5 Number theory (11-XX) 4 Manifolds and cell complexes (57-XX) 4 Mathematics education (97-XX) 3 Algebraic geometry (14-XX) 3 Functions of a complex variable (30-XX) 2 Mathematical logic and foundations (03-XX) 2 Field theory and polynomials (12-XX) 2 Commutative algebra (13-XX) 2 Measure and integration (28-XX) 2 Abstract harmonic analysis (43-XX) 1 (04-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX)

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