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## 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: 149 Publications since 1973, including 16 Books 5 Contributions as Editor 1 Further Contribution Reviewing Activity: 231 Reviews Biographic References: 1 Publication
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#### Co-Authors

 26 single-authored 46 Lubich, Christian 30 Wanner, Gerhard 11 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 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 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 Skeel, Robert D. 1 Söderlind, Gustaf 1 Stoffer, Daniel 1 Türke, Helmut 1 Weiss, Daniel A. 1 Zugck, J.
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#### Serials

 23 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 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 Numerical Algorithms 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 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

 139 Numerical analysis (65-XX) 72 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) 4 Approximations and expansions (41-XX) 4 Optics, electromagnetic theory (78-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 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

143 Publications have been cited 7,600 times in 5,115 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
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
Long-time energy conservation of numerical methods for oscillatory differential equations. Zbl 0988.65118
Hairer, Ernst; Lubich, Christian
2000
Geometric numerical integration illustrated by the Störmer-Verlet method. Zbl 1046.65110
Hairer, Ernst; Lubich, Christian; Wanner, Gerhard
2003
Energy-preserving variant of collocation methods. Zbl 1432.65185
Hairer, E.
2010
Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations. Zbl 0657.65093
Hairer, E.; Lubich, Ch.; Roche, M.
1988
A theory for Nyström methods. Zbl 0307.65053
Hairer, Ernst; Wanner, Gerhard
1976
One-step and extrapolation methods for differential-algebraic systems. Zbl 0635.65083
Deuflhard, P.; Hairer, E.; Zugck, J.
1987
Fast numerical solution of nonlinear Volterra convolution equations. Zbl 0581.65095
Hairer, E.; Lubich, Ch.; Schlichte, M.
1985
The life-span of backward error analysis for numerical integrators. Zbl 0874.65061
Hairer, E.; Lubich, Ch.
1997
Backward analysis of numerical integrators and symplectic methods. Zbl 0828.65097
Hairer, Ernst
1994
Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations. Zbl 1163.65066
Cohen, David; Hairer, Ernst; Lubich, Christian
2008
Linear energy-preserving integrators for Poisson systems. Zbl 1216.65175
Cohen, David; Hairer, Ernst
2011
Nonlinear convergence analysis for the parareal algorithm. Zbl 1140.65336
Gander, Martin J.; Hairer, Ernst
2008
Stiff differential equations solved by Radau methods. Zbl 0945.65080
Hairer, Ernst; Wanner, Gerhard
1999
Algebraically stable and implementable Runge-Kutta methods of high order. Zbl 0533.65041
Hairer, Ernst; Wanner, Gerhard
1981
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
Implementing Radau IIA methods for stiff delay differential equations. Zbl 0986.65069
Guglielmi, N.; Hairer, E.
2001
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
Algebraic structures of B-series. Zbl 1201.65124
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
2010
Méthodes de Nystrom pour l’équation différentielle y”=f(x,y). Zbl 0325.65033
Hairer, Ernst
1977
Error of Rosenbrock methods for stiff problems studied via differential algebraic equations. Zbl 0674.65039
Hairer, E.; Lubich, Ch.; Roche, M.
1989
Order conditions for numerical methods for partitioned ordinary differential equations. Zbl 0462.65049
Hairer, E.
1981
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
Half-explicit Runge-Kutta methods for differential-algebraic systems of index 2. Zbl 0785.65082
Brasey, V.; Hairer, E.
1993
Numerical energy conservation for multi-frequency oscillatory differential equations. Zbl 1083.65117
Cohen, D.; Hairer, E.; Lubich, Ch.
2005
Computing breaking points in implicit delay differential equations. Zbl 1160.65041
Guglielmi, Nicola; Hairer, Ernst
2008
Unconditionally stable explicit methods for parabolic equations. Zbl 0454.65052
Hairer, E.
1980
Variable time step integration with symplectic methods. Zbl 0884.65073
Hairer, E.
1997
Fast numerical solution of weakly singular Volterra integral equations. Zbl 0654.65091
Hairer, E.; Lubich, Ch.; Schlichte, M.
1988
Energy-diminishing integration of gradient systems. Zbl 1321.65115
Hairer, Ernst; Lubich, Christian
2014
Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions. Zbl 1145.35087
Cohen, David; Hairer, Ernst; Lubich, Christian
2008
Order stars and stability for delay differential equations. Zbl 0937.65079
Guglielmi, Nicola; Hairer, Ernst
1999
Asymptotic expansions of the global error of fixed-stepsize methods. Zbl 0571.65066
Hairer, E.; Lubich, C.
1984
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
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
Order conditions for general two-step Runge-Kutta methods. Zbl 0890.65077
Hairer, Ernst; Wanner, Gerhard
1997
Symmetric projection methods for differential equations on manifolds. Zbl 0968.65108
Hairer, E.
2000
Analysis for parareal algorithms applied to Hamiltonian differential equations. Zbl 1291.65209
Gander, Martin J.; Hairer, Ernst
2014
Accurate long-term integration of dynamical systems. Zbl 0837.65071
Calvo, M. P.; Hairer, E.
1995
Spectral semi-discretisations of weakly non-linear wave equations over long times. Zbl 1156.35007
Hairer, E.; Lubich, C.
2008
Modulated Fourier expansions of highly oscillatory differential equations. Zbl 1056.34005
Cohen, David; Hairer, Ernst; Lubich, Christian
2003
Highly oscillatory problems. Zbl 1170.37002
2009
Explicit, time reversible, adaptive step size control. Zbl 1081.65117
Hairer, Ernst; Söderlind, Gustaf
2005
Achieving Brouwer’s law with implicit Runge-Kutta methods. Zbl 1148.65058
Hairer, E.; McLachlan, R. I.; Razakarivony, A.
2008
Geometric proofs of numerical stability for delay equations. Zbl 0976.65077
Guglielmi, Nicola; Hairer, Ernst
2001
Analysis by its history. Zbl 0842.26002
Hairer, E.; Wanner, G.
1995
On conjugate symplecticity of B-series integrators. Zbl 1329.65307
Hairer, Ernst; Zbinden, Christophe J.
2013
Classification of hidden dynamics in discontinuous dynamical systems. Zbl 1329.34028
Guglielmi, Nicola; Hairer, Ernst
2015
Numerical integrators based on modified differential equations. Zbl 1122.65059
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
2007
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
Long-term stability of multi-value methods for ordinary differential equations. Zbl 1312.65111
D’Ambrosio, R.; Hairer, E.
2014
G-symplecticity implies conjugate-symplecticity of the underlying one-step method. Zbl 1282.65168
D’Ambrosio, R.; Hairer, E.; Zbinden, C. J.
2013
Backward error analysis for multistep methods. Zbl 0941.65077
Hairer, Ernst
1999
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
Energy behaviour of the Boris method for charged-particle dynamics. Zbl 1404.65309
Hairer, Ernst; Lubich, Christian
2018
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
On energy conservation of the simplified Takahashi-Imada method. Zbl 1172.65067
Hairer, Ernst; McLachlan, Robert I.; Skeel, Robert D.
2009
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
The equivalence of B-stability and A-stability. Zbl 0571.65060
Hairer, E.; Türke, H.
1984
The non-existence of symplectic multi-derivative Runge-Kutta methods. Zbl 0816.65043
Hairer, E.; Murua, A.; Sanz-Serna, J. M.
1994
Symmetric multistep methods for charged-particle dynamics. Zbl 1416.78037
Hairer, Ernst; Lubich, Christian
2017
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
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
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
Oscillation over long times in numerical Hamiltonian systems. Zbl 1180.37121
Hairer, Ernst; Lubich, Christian
2009
A necessary condition for BSI-stability. Zbl 0579.65091
Dekker, Kees; Hairer, Ernst
1985
Order barriers for symplectic multi-value methods. Zbl 0902.65027
Hairer, E.; Leone, P.
1998
Symmetric linear multistep. Zbl 1149.65054
Hairer, Ernst
2006
On error growth functions of Runge-Kutta methods. Zbl 0871.65071
Hairer, E.; Zennaro, M.
1996
Implicit Runge-Kutta methods for higher index differential-algebraic systems. Zbl 0834.65062
Hairer, E.; Jay, L.
1993
Energy conservation by Störmer-type numerical integrators. Zbl 0952.65053
Hairer, E.; Lubich, Ch.
2000
Numerical methods for singular nonlinear integrodifferential equations. Zbl 0631.65142
Hairer, E.; Maass, P.
1987
Energy separation in oscillatory Hamiltonian systems without any non-resonance condition. Zbl 1329.70045
Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian
2013
On the order of iterated defect correction. An algebraic proof. Zbl 0414.65045
Hairer, E.
1978
Asymptotic expansions and backward analysis for numerical integrators. Zbl 0942.65092
Hairer, Ernst; Lubich, Christian
2000
Invariant tori of dissipatively perturbed Hamiltonian systems under symplectic discretization. Zbl 1022.37042
Hairer, Ernst; Lubich, Christian
1999
Dense output for extrapolation methods. Zbl 0693.65048
Hairer, Ernst; Ostermann, Alexander
1990
On the instability of the BDF formulas. Zbl 0538.65051
Hairer, Ernst; Wanner, Gerhard
1983
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
Constructive characterization of A-stable approximations to exp(z) and its connection with algebraically stable Runge-Kutta methods. Zbl 0493.65035
Hairer, E.
1982
Power boundedness in the maximum norm of stability matrices for ADI methods. Zbl 07381114
González-Pinto, S.; Hairer, E.; Hernández-Abreu, D.
2021
Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field. Zbl 1432.78013
Hairer, Ernst; Lubich, Christian
2020
A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field. Zbl 1434.65312
Hairer, Ernst; Lubich, Christian; Wang, Bin
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
Regularization of neutral delay differential equations with several delays. Zbl 1283.34074
Guglielmi, Nicola; Hairer, Ernst
2013
Long-term control of oscillations in differential equations. Zbl 1338.65182
Hairer, Ernst; Lubich, Christian
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
Spectral semi-discretisations of weakly non-linear wave equations over long times. Zbl 1156.35007
Hairer, E.; Lubich, C.
2008
Achieving Brouwer’s law with implicit Runge-Kutta methods. Zbl 1148.65058
Hairer, E.; McLachlan, R. I.; Razakarivony, A.
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
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
Order of convergence of Runge-Kutta methods for stiff and differential- algebraic problems. Zbl 0731.65062
Hairer, Ernst
1991
...and 43 more Documents
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#### Cited by 5,346 Authors

 75 Wu, Xinyuan 71 Hairer, Ernst 70 Lubich, Christian 60 Weiner, Rüdiger 57 Jackiewicz, Zdzislaw 41 Butcher, John C. 41 Simos, Theodore E. 40 Ostermann, Alexander 37 Wang, Yushun 35 Wang, Bin 33 Brugnano, Luigi 32 Chartier, Philippe 31 Ramos, Higinio 31 You, Xiong 30 Montijano, Juan Ignacio 30 Sanz-Serna, Jesús María 29 Sandu, Adrian 28 Auzinger, Winfried 27 González-Pinto, Severiano 27 Murua, Ander 27 van der Houwen, Pieter J. 27 Xiao, Aiguo 26 D’Ambrosio, Raffaele 26 Iserles, Arieh 26 Kulikov, Gennady Yur’evich 26 Rández, Luis 26 Van Daele, Marnix 25 Fang, Yonglei 25 Faou, Erwan 25 Hundsdorfer, Willem H. 24 Calvo, Manuel 24 Sommeijer, Ben P. 24 Vanden Berghe, Guido 23 Abdi, Ali 23 Burrage, Kevin 23 Casas, Fernando 23 Franco, J. Méndez 23 Tsitouras, Charalampos 22 Blanes, Sergio 22 Cong, Nguyen Huu 22 Iavernaro, Felice 22 Paternoster, Beatrice 22 Podhaisky, Helmut 22 Schmitt, Bernhard A. 21 McLachlan, Robert I. 21 Shi, Wei 21 Vigo-Aguiar, Jesus 21 Zhang, Chengjian 20 Arnold, Martin 20 Gan, Siqing 20 Hojjati, Gholamreza 20 Huang, Chengming 20 Li, Jiyong 20 Owren, Brynjulf 20 Shampine, Lawrence Fred 20 Sun, Yajuan 20 Verwer, Jan G. 19 Hong, Jialin 19 Li, Shoufu 19 Mehrmann, Volker 19 Strehmel, Karl 18 Celledoni, Elena 18 Hernandez-Abreu, Domingo 18 Higueras, Inmaculada 18 Jator, Samuel N. 18 Leok, Melvin 18 Martín de Diego, David 18 Simeon, Bernd 18 Vilmart, Gilles 18 Wanner, Gerhard 17 Akrivis, Georgios D. 17 Hartmann, Stefan 17 Tian, Hongjiong 17 Wang, Wansheng 17 Zhao, Jingjun 16 Conte, Dajana 16 Guglielmi, Nicola 16 Higham, Desmond J. 16 Ismail, Fudziah Bt. 16 Karasözen, Bülent 16 Nørsett, Syvert Paul 16 Rogov, Boris V. 16 Söderlind, Gustaf 16 Spijker, Marc N. 15 De Meyer, Hans E. 15 Gander, Martin Jakob 15 Koch, Othmar 15 Senu, Norazak 15 Thalhammer, Mechthild 15 Wu, Shulin 14 Boscarino, Sebastiano 14 Brunner, Hermann 14 Campbell, Stephen LaVern 14 Chan, Robert Peng Kong 14 Famelis, Ioannis Th. 14 Gong, Yuezheng 14 Günther, Michael 14 Hochbruck, Marlis 14 Izzo, Giuseppe 14 Jiang, Yaolin ...and 5,246 more Authors
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#### Cited in 457 Serials

 502 Journal of Computational and Applied Mathematics 479 Applied Numerical Mathematics 263 Journal of Computational Physics 258 BIT 219 Applied Mathematics and Computation 155 Numerische Mathematik 154 Numerical Algorithms 137 Journal of Scientific Computing 135 Computers & Mathematics with Applications 105 Computer Methods in Applied Mechanics and Engineering 100 SIAM Journal on Scientific Computing 90 Mathematics of Computation 83 International Journal of Computer Mathematics 75 SIAM Journal on Numerical Analysis 62 Computer Physics Communications 60 Mathematics and Computers in Simulation 55 International Journal for Numerical Methods in Engineering 50 Computing 50 Foundations of Computational Mathematics 44 Multibody System Dynamics 42 Applied Mathematics Letters 33 Celestial Mechanics and Dynamical Astronomy 33 Communications in Nonlinear Science and Numerical Simulation 32 Advances in Computational Mathematics 30 Computers and Fluids 30 Physica D 30 Computational and Applied Mathematics 29 Physics Letters. A 29 Journal of Mathematical Chemistry 25 Computational Mechanics 25 Mathematical and Computer Modelling 25 Computational Mathematics and Mathematical Physics 25 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 24 Discrete and Continuous Dynamical Systems 23 Calcolo 23 Numerical Methods for Partial Differential Equations 23 Mathematical Problems in Engineering 22 Nonlinear Dynamics 21 Applied Mathematical Modelling 21 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 20 Japan Journal of Industrial and Applied Mathematics 18 Linear Algebra and its Applications 17 Journal of Mathematical Analysis and Applications 17 Journal of Nonlinear Science 17 Discrete and Continuous Dynamical Systems. Series B 16 Communications in Computational Physics 15 Doklady Mathematics 15 Abstract and Applied Analysis 15 Journal of Applied Mathematics 14 Journal of Applied Mathematics and Computing 14 Multiscale Modeling & Simulation 13 Journal of Optimization Theory and Applications 13 International Journal of Modern Physics C 13 Differential Equations 13 Advances in Difference Equations 13 BIT. Nordisk Tidskrift for Informationsbehandling 12 Chaos, Solitons and Fractals 12 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 12 Journal of Difference Equations and Applications 12 Optimization Methods & Software 12 Regular and Chaotic Dynamics 12 Discrete and Continuous Dynamical Systems. Series S 12 Journal of Computational Dynamics 11 Mathematical Biosciences 11 Journal of Differential Equations 11 Journal of Mathematical Sciences (New York) 11 Numerical Linear Algebra with Applications 10 International Journal for Numerical Methods in Fluids 10 Journal of Mathematical Physics 10 Applied Mathematics and Mechanics. (English Edition) 10 Journal of Dynamics and Differential Equations 10 Chaos 10 Combustion Theory and Modelling 10 Advances in Applied Mathematics and 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 9 Matematicheskoe Modelirovanie 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 SIAM Journal on Control and Optimization 8 Systems & Control Letters 8 SIAM Journal on Matrix Analysis and Applications 8 Mediterranean Journal of Mathematics 8 Acta Numerica 8 Journal of Theoretical Biology 8 International Journal of Applied and Computational Mathematics 7 Journal of Fluid Mechanics 7 Bulletin of Mathematical Biology 7 Automatica 7 International Journal of Circuit Theory and Applications 7 Meccanica 7 Journal of Complexity 7 Journal of Computational Neuroscience 7 Discrete Dynamics in Nature and Society 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 SIAM Journal on Applied Dynamical Systems 7 Frontiers of Mathematics in China ...and 357 more Serials
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#### Cited in 58 Fields

 4,030 Numerical analysis (65-XX) 1,682 Ordinary differential equations (34-XX) 946 Partial differential equations (35-XX) 556 Dynamical systems and ergodic theory (37-XX) 441 Mechanics of particles and systems (70-XX) 403 Fluid mechanics (76-XX) 237 Probability theory and stochastic processes (60-XX) 233 Mechanics of deformable solids (74-XX) 201 Biology and other natural sciences (92-XX) 152 Systems theory; control (93-XX) 140 Integral equations (45-XX) 125 Calculus of variations and optimal control; optimization (49-XX) 121 Statistical mechanics, structure of matter (82-XX) 105 Quantum theory (81-XX) 96 Optics, electromagnetic theory (78-XX) 89 Computer science (68-XX) 81 Classical thermodynamics, heat transfer (80-XX) 69 Operations research, mathematical programming (90-XX) 58 Operator theory (47-XX) 56 Linear and multilinear algebra; matrix theory (15-XX) 51 Approximations and expansions (41-XX) 50 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 48 Statistics (62-XX) 48 Information and communication theory, circuits (94-XX) 44 Differential geometry (53-XX) 36 Geophysics (86-XX) 35 Real functions (26-XX) 31 Difference and functional equations (39-XX) 30 Combinatorics (05-XX) 21 Associative rings and algebras (16-XX) 21 Astronomy and astrophysics (85-XX) 20 Relativity and gravitational theory (83-XX) 19 Global analysis, analysis on manifolds (58-XX) 18 Nonassociative rings and algebras (17-XX) 17 History and biography (01-XX) 17 Integral transforms, operational calculus (44-XX) 14 Topological groups, Lie groups (22-XX) 12 Functional analysis (46-XX) 9 General and overarching topics; collections (00-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 8 Special functions (33-XX) 4 Geometry (51-XX) 4 Manifolds and cell complexes (57-XX) 3 Number theory (11-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 Abstract harmonic analysis (43-XX) 2 Mathematics education (97-XX) 1 Category theory; homological algebra (18-XX) 1 Measure and integration (28-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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