Edit Profile (opens in new tab) Hairer, Ernst Co-Author Distance 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: 157 Publications since 1973, including 16 Books and 2 Additional arXiv Preprints 5 Contributions as Editor · 1 Further Contribution Reviewing Activity: 231 Reviews Biographic References: 1 Publication Co-Authors: 51 Co-Authors with 136 Joint Publications 1,620 Co-Co-Authors all top 5 Co-Authors 26 single-authored 48 Lubich, Christian 30 Wanner, Gerhard 14 Guglielmi, Nicola 9 Nørsett, Syvert Paul 7 Iserles, Arieh 5 Gauckler, Ludwig J. 5 González-Pinto, Severiano 5 Hernandez-Abreu, Domingo 5 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 Shi, Yanyan 2 Zbinden, Christophe J. 2 Zennaro, Marino 1 Beyn, Wolf-Jürgen 1 Brunner, Hermann 1 Caboussat, Alexandre 1 Chyba, Monique 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 Skeel, Robert D. 1 Söderlind, Gustaf 1 Stoffer, Daniel 1 Türke, Helmut 1 Wang, Bin 1 Weiss, Daniel Alexander 1 Zugck, J. all top 5 Serials 24 Numerische Mathematik 19 BIT 9 SIAM Journal on Numerical Analysis 9 Springer Series in Computational Mathematics 7 Journal of Computational and Applied Mathematics 7 Applied Numerical 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 Numerical Algorithms 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 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 Progress in Scientific Computing 1 SCOPOS 1 JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics 1 SMAI Journal of Computational Mathematics 1 Springer-Lehrbuch all top 5 Fields 145 Numerical analysis (65-XX) 74 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) 8 Integral equations (45-XX) 7 Real functions (26-XX) 6 History and biography (01-XX) 6 Optics, electromagnetic theory (78-XX) 5 General and overarching topics; collections (00-XX) 4 Approximations and expansions (41-XX) 2 Functions of a complex variable (30-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Linear and multilinear algebra; matrix theory (15-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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 153 Publications have been cited 10,735 times in 7,189 Documents Cited by ▼ Year ▼ Solving ordinary differential equations. I: Nonstiff problems. 2. rev. ed. Zbl 0789.65048 Hairer, Ernst; Nørsett, Syvert P.; Wanner, Gerhard 1,670 1993 Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. 2nd ed. Zbl 1094.65125 Hairer, Ernst; Lubich, Christian; Wanner, Gerhard 1,457 2006 Solving ordinary differential equations. II: Stiff and differential-algebraic problems. 2nd rev. ed. Zbl 0859.65067 Hairer, Ernst; Wanner, Gerhard 1,435 1996 Solving ordinary differential equations II: Stiff and differential-algebraic problems. Zbl 0729.65051 Hairer, Ernst; Wanner, Gerhard 825 1991 Solving ordinary differential equations. I: Nonstiff problems. Zbl 0638.65058 Hairer, Ernst; Nørsett, Syvert P.; Wanner, Gerhard 637 1987 Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. Zbl 0994.65135 Hairer, Ernst; Lubich, Christian; Wanner, Gerhard 609 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 355 2010 The numerical solution of differential-algebraic systems by Runge-Kutta methods. Zbl 0683.65050 Hairer, Ernst; Lubich, Christian; Roche, Michel 221 1989 Solving ordinary differential equations. I: Nonstiff problems. 2nd revised ed., 3rd corrected printing. Zbl 1185.65115 Hairer, Ernst; Nørsett, Syvert P.; Wanner, Gerhard 170 2010 Geometric numerical integration illustrated by the Störmer-Verlet method. Zbl 1046.65110 Hairer, Ernst; Lubich, Christian; Wanner, Gerhard 145 2003 Energy-preserving variant of collocation methods. Zbl 1432.65185 Hairer, E. 131 2010 Order stars and stability theorems. Zbl 0444.65039 Wanner, Gerhard; Hairer, Ernst; Nørsett, Syvert P. 124 1978 Long-time energy conservation of numerical methods for oscillatory differential equations. Zbl 0988.65118 Hairer, Ernst; Lubich, Christian 117 2000 Unconditionally stable methods for second order differential equations. Zbl 0393.65035 Hairer, E. 105 1979 On the Butcher group and general multi-value methods. Zbl 0293.65050 Hairer, Ernst; Wanner, Gerhard 99 1974 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 95 2010 Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations. Zbl 0657.65093 Hairer, E.; Lubich, Ch.; Roche, M. 84 1988 Linear energy-preserving integrators for Poisson systems. Zbl 1216.65175 Cohen, David; Hairer, Ernst 83 2011 Nonlinear convergence analysis for the parareal algorithm. Zbl 1140.65336 Gander, Martin J.; Hairer, Ernst 82 2008 Fast numerical solution of nonlinear Volterra convolution equations. Zbl 0581.65095 Hairer, E.; Lubich, Ch.; Schlichte, M. 78 1985 Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations. Zbl 1163.65066 Cohen, David; Hairer, Ernst; Lubich, Christian 68 2008 A theory for Nyström methods. Zbl 0307.65053 Hairer, Ernst; Wanner, Gerhard 67 1976 Stiff differential equations solved by Radau methods. Zbl 0945.65080 Hairer, Ernst; Wanner, Gerhard 61 1999 Algebraic structures of B-series. Zbl 1201.65124 Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles 61 2010 The life-span of backward error analysis for numerical integrators. Zbl 0874.65061 Hairer, E.; Lubich, Ch. 57 1997 One-step and extrapolation methods for differential-algebraic systems. Zbl 0635.65083 Deuflhard, P.; Hairer, E.; Zugck, J. 57 1987 Backward analysis of numerical integrators and symplectic methods. Zbl 0828.65097 Hairer, Ernst 54 1994 Implementing Radau IIA methods for stiff delay differential equations. Zbl 0986.65069 Guglielmi, N.; Hairer, E. 49 2001 Multistep-multistage-multiderivative methods for ordinary differential equations. Zbl 0271.65048 Hairer, Ernst; Wanner, Gerhard 44 1973 Algebraically stable and implementable Runge-Kutta methods of high order. Zbl 0533.65041 Hairer, Ernst; Wanner, Gerhard 43 1981 Order conditions for numerical methods for partitioned ordinary differential equations. Zbl 0462.65049 Hairer, E. 40 1981 Computing breaking points in implicit delay differential equations. Zbl 1160.65041 Guglielmi, Nicola; Hairer, Ernst 40 2008 On the stability of semi-implicit methods for ordinary differential equations. Zbl 0489.65046 Hairer, E.; Bader, G.; Lubich, Ch. 39 1982 Energy-diminishing integration of gradient systems. Zbl 1321.65115 Hairer, Ernst; Lubich, Christian 38 2014 Half-explicit Runge-Kutta methods for differential-algebraic systems of index 2. Zbl 0785.65082 Brasey, V.; Hairer, E. 38 1993 Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions. Zbl 1145.35087 Cohen, David; Hairer, Ernst; Lubich, Christian 37 2008 Runge-Kutta theory for Volterra integral equations of the second kind. Zbl 0496.65066 Brunner, Hermann; Hairer, Ernst; Nørsett, Syvert P. 36 1982 Error of Rosenbrock methods for stiff problems studied via differential algebraic equations. Zbl 0674.65039 Hairer, E.; Lubich, Ch.; Roche, M. 36 1989 Energy conservation with non-symplectic methods: examples and counter-examples. Zbl 1082.65132 Faou, Erwan; Hairer, Ernst; Pham, Truong-Linh 35 2004 Numerical energy conservation for multi-frequency oscillatory differential equations. Zbl 1083.65117 Cohen, D.; Hairer, E.; Lubich, Ch. 35 2005 Variable time step integration with symplectic methods. Zbl 0884.65073 Hairer, E. 34 1997 Méthodes de Nystrom pour l’équation différentielle y”=f(x,y). Zbl 0325.65033 Hairer, Ernst 34 1977 Modulated Fourier expansions of highly oscillatory differential equations. Zbl 1056.34005 Cohen, David; Hairer, Ernst; Lubich, Christian 33 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. 33 1983 Fast numerical solution of weakly singular Volterra integral equations. Zbl 0654.65091 Hairer, E.; Lubich, Ch.; Schlichte, M. 32 1988 A one-step method of order 10 for y”=f(x,y). Zbl 0482.65042 Hairer, E. 31 1982 Analysis for parareal algorithms applied to Hamiltonian differential equations. Zbl 1291.65209 Gander, Martin J.; Hairer, Ernst 30 2014 Order stars and stability for delay differential equations. Zbl 0937.65079 Guglielmi, Nicola; Hairer, Ernst 29 1999 Highly oscillatory problems. Zbl 1170.37002 29 2009 A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field. Zbl 1434.65312 Hairer, Ernst; Lubich, Christian; Wang, Bin 29 2020 Achieving Brouwer’s law with implicit Runge-Kutta methods. Zbl 1148.65058 Hairer, E.; McLachlan, R. I.; Razakarivony, A. 29 2008 Symmetric projection methods for differential equations on manifolds. Zbl 0968.65108 Hairer, E. 28 2000 Symmetric multistep methods over long times. Zbl 1060.65074 Hairer, Ernst; Lubich, Christian 27 2004 Unconditionally stable explicit methods for parabolic equations. Zbl 0454.65052 Hairer, E. 27 1980 Asymptotic expansions of the global error of fixed-stepsize methods. Zbl 0571.65066 Hairer, E.; Lubich, C. 26 1984 Energy behaviour of the Boris method for charged-particle dynamics. Zbl 1404.65309 Hairer, Ernst; Lubich, Christian 26 2018 Symmetric multistep methods for charged-particle dynamics. Zbl 1416.78037 Hairer, Ernst; Lubich, Christian 26 2017 Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field. Zbl 1432.78013 Hairer, Ernst; Lubich, Christian 25 2020 GniCodes –Matlab programs for geometric numerical integration. Zbl 1028.65136 Hairer, Ernst; Hairer, Martin 24 2003 Classification of hidden dynamics in discontinuous dynamical systems. Zbl 1329.34028 Guglielmi, Nicola; Hairer, Ernst 24 2015 Spectral semi-discretisations of weakly non-linear wave equations over long times. Zbl 1156.35007 Hairer, E.; Lubich, C. 24 2008 Order conditions for general two-step Runge-Kutta methods. Zbl 0890.65077 Hairer, Ernst; Wanner, Gerhard 23 1997 Accurate long-term integration of dynamical systems. Zbl 0837.65071 Calvo, M. P.; Hairer, E. 22 1995 Explicit, time reversible, adaptive step size control. Zbl 1081.65117 Hairer, Ernst; Söderlind, Gustaf 20 2005 Numerical integrators based on modified differential equations. Zbl 1122.65059 Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles 20 2007 Long-term stability of multi-value methods for ordinary differential equations. Zbl 1312.65111 D’Ambrosio, R.; Hairer, E. 19 2014 Geometric proofs of numerical stability for delay equations. Zbl 0976.65077 Guglielmi, Nicola; Hairer, Ernst 18 2001 Analysis by its history. Zbl 0842.26002 Hairer, E.; Wanner, G. 17 1995 Backward error analysis for multistep methods. Zbl 0941.65077 Hairer, Ernst 16 1999 On conjugate symplecticity of B-series integrators. Zbl 1329.65307 Hairer, Ernst; Zbinden, Christophe J. 16 2013 Long-term analysis of the Störmer-Verlet method for Hamiltonian systems with a solution-dependent high frequency. Zbl 1408.65100 Hairer, Ernst; Lubich, Christian 16 2016 Highest possible order of algebraically stable diagonally implicit Runge- Kutta methods. Zbl 0425.65037 Hairer, E. 15 1980 AMF-type W-methods for parabolic problems with mixed derivatives. Zbl 1397.65159 González-Pinto, S.; Hairer, E.; Hernández-Abreu, D.; Pérez-Rodríguez, S. 15 2018 G-symplecticity implies conjugate-symplecticity of the underlying one-step method. Zbl 1282.65168 D’Ambrosio, R.; Hairer, E.; Zbinden, C. J. 14 2013 Report 14/2006: Geometric Numerical Integration (March 19th – March 25th, 2006). Zbl 1109.65301 14 2006 Equilibria of Runge-Kutta methods. Zbl 0693.65047 Hairer, E.; Iserles, A.; Sanz-Serna, J. M. 13 1990 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 13 2015 On the stability of Volterra-Runge-Kutta methods. Zbl 0532.65086 Hairer, E.; Lubich, Ch. 12 1984 Extrapolation at stiff differential equations. Zbl 0643.65034 Hairer, E.; Lubich, C. 11 1988 On energy conservation of the simplified Takahashi-Imada method. Zbl 1172.65067 Hairer, Ernst; McLachlan, Robert I.; Skeel, Robert D. 11 2009 Reversible long-term integration with variable stepsizes. Zbl 0871.65075 Hairer, Ernst; Stoffer, Daniel 10 1997 Order barriers for symplectic multi-value methods. Zbl 0902.65027 Hairer, E.; Leone, P. 10 1998 Solving optimization-constrained differential equations with discontinuity points, with application to atmospheric chemistry. Zbl 1391.86007 Landry, Chantal; Caboussat, Alexandre; Hairer, Ernst 10 2009 On the energy distribution in Fermi-Pasta-Ulam lattices. Zbl 1283.70011 Hairer, Ernst; Lubich, Christian 10 2012 Oscillation over long times in numerical Hamiltonian systems. Zbl 1180.37121 Hairer, Ernst; Lubich, Christian 10 2009 The non-existence of symplectic multi-derivative Runge-Kutta methods. Zbl 0816.65043 Hairer, E.; Murua, A.; Sanz-Serna, J. M. 9 1994 On error growth functions of Runge-Kutta methods. Zbl 0871.65071 Hairer, E.; Zennaro, M. 9 1996 The equivalence of B-stability and A-stability. Zbl 0571.65060 Hairer, E.; Türke, H. 9 1984 Energy separation in oscillatory Hamiltonian systems without any non-resonance condition. Zbl 1329.70045 Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian 9 2013 Asymptotic expansions for regularized state-dependent neutral delay equations. Zbl 1257.34060 Guglielmi, Nicola; Hairer, Ernst 9 2012 Numerical stability in the presence of variable coefficients. Zbl 1347.65144 Hairer, Ernst; Iserles, Arieh 9 2016 Energy conservation by Störmer-type numerical integrators. Zbl 0952.65053 Hairer, E.; Lubich, Ch. 8 2000 A necessary condition for BSI-stability. Zbl 0579.65091 Dekker, Kees; Hairer, Ernst 8 1985 Modulated Fourier expansions for continuous and discrete oscillatory systems. Zbl 1316.42005 Hairer, Ernst; Lubich, Christian 8 2013 Numerical methods for singular nonlinear integrodifferential equations. Zbl 0631.65142 Hairer, E.; Maass, P. 8 1987 Conjugate-symplecticity of linear multistep methods. Zbl 1174.65055 Hairer, Ernst 8 2008 Analysis by its history. Corr. 4th printing. Zbl 1139.26001 Hairer, Ernst; Wanner, Gerhard 8 2008 Symmetric linear multistep. Zbl 1149.65054 Hairer, Ernst 8 2006 Preprocessed discrete Moser-Veselov algorithm for the full dynamics of a rigid body. Zbl 1127.70002 Hairer, Ernst; Vilmart, Gilles 8 2006 Large-stepsize integrators for charged-particle dynamics over multiple time scales. Zbl 1510.65314 Hairer, Ernst; Lubich, Christian; Shi, Yanyan 8 2022 High order PDE-convergence of AMF-W methods for 2D-linear parabolic problems. Zbl 1496.65141 González-Pinto, S.; Hairer, E.; Hernández-Abreu, D. 2 2023 Sliding modes of high codimension in piecewise-smooth dynamical systems. Zbl 07730428 Guglielmi, Nicola; Hairer, Ernst 1 2023 Large-stepsize integrators for charged-particle dynamics over multiple time scales. Zbl 1510.65314 Hairer, Ernst; Lubich, Christian; Shi, Yanyan 8 2022 An efficient algorithm for solving piecewise-smooth dynamical systems. Zbl 1485.65078 Guglielmi, Nicola; Hairer, Ernst 2 2022 Power boundedness in the maximum norm of stability matrices for ADI methods. Zbl 1495.65133 González-Pinto, S.; Hairer, E.; Hernández-Abreu, D. 2 2021 A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field. Zbl 1434.65312 Hairer, Ernst; Lubich, Christian; Wang, Bin 29 2020 Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field. Zbl 1432.78013 Hairer, Ernst; Lubich, Christian 25 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 5 2020 On conjectures of Stenger in the theory of orthogonal polynomials. Zbl 1499.33038 Gautschi, Walter; Hairer, Ernst 3 2019 Energy behaviour of the Boris method for charged-particle dynamics. Zbl 1404.65309 Hairer, Ernst; Lubich, Christian 26 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. 15 2018 Dynamics, numerical analysis, and some geometry. Zbl 1451.62056 Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian 8 2018 PDE-W-methods for parabolic problems with mixed derivatives. Zbl 1447.65060 González-Pinto, S.; Hairer, E.; Hernández-Abreu, D.; Pérez-Rodríguez, S. 6 2018 Symmetric multistep methods for charged-particle dynamics. Zbl 1416.78037 Hairer, Ernst; Lubich, Christian 26 2017 Solutions leaving a codimension-\(2\) sliding. Zbl 1375.34025 Guglielmi, Nicola; Hairer, Ernst 6 2017 Banded, stable, skew-symmetric differentiation matrices of high order. Zbl 1433.65138 Hairer, Ernst; Iserles, Arieh 3 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 16 2016 Numerical stability in the presence of variable coefficients. Zbl 1347.65144 Hairer, Ernst; Iserles, Arieh 9 2016 Long-term analysis of semilinear wave equations with slowly varying wave speed. Zbl 1368.35164 Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian 5 2016 Path-regularization of linear neutral delay differential equations with several delays. Zbl 1343.34153 Guglielmi, Nicola; Hairer, Ernst 2 2016 Classification of hidden dynamics in discontinuous dynamical systems. Zbl 1329.34028 Guglielmi, Nicola; Hairer, Ernst 24 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 13 2015 Energy-diminishing integration of gradient systems. Zbl 1321.65115 Hairer, Ernst; Lubich, Christian 38 2014 Analysis for parareal algorithms applied to Hamiltonian differential equations. Zbl 1291.65209 Gander, Martin J.; Hairer, Ernst 30 2014 Long-term stability of multi-value methods for ordinary differential equations. Zbl 1312.65111 D’Ambrosio, R.; Hairer, E. 19 2014 Numerical approaches for state-dependent neutral delay equations with discontinuities. Zbl 1533.65094 Guglielmi, Nicola; Hairer, Ernst 6 2014 Long-term stability of symmetric partitioned linear multistep methods. Zbl 1318.65078 Console, Paola; Hairer, Ernst 3 2014 Challenges in geometric numerical integration. Zbl 1325.65174 Hairer, Ernst 2 2014 On conjugate symplecticity of B-series integrators. Zbl 1329.65307 Hairer, Ernst; Zbinden, Christophe J. 16 2013 G-symplecticity implies conjugate-symplecticity of the underlying one-step method. Zbl 1282.65168 D’Ambrosio, R.; Hairer, E.; Zbinden, C. J. 14 2013 Energy separation in oscillatory Hamiltonian systems without any non-resonance condition. Zbl 1329.70045 Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian 9 2013 Modulated Fourier expansions for continuous and discrete oscillatory systems. Zbl 1316.42005 Hairer, Ernst; Lubich, Christian 8 2013 Symmetric multistep methods for constrained Hamiltonian systems. Zbl 1290.65125 Console, Paola; Hairer, Ernst; Lubich, Christian 5 2013 Regularization of neutral delay differential equations with several delays. Zbl 1283.34074 Guglielmi, Nicola; Hairer, Ernst 3 2013 Long-term control of oscillations in differential equations. Zbl 1338.65182 Hairer, Ernst; Lubich, Christian 3 2013 On the energy distribution in Fermi-Pasta-Ulam lattices. Zbl 1283.70011 Hairer, Ernst; Lubich, Christian 10 2012 Asymptotic expansions for regularized state-dependent neutral delay equations. Zbl 1257.34060 Guglielmi, Nicola; Hairer, Ernst 9 2012 Metastable energy strata in weakly nonlinear wave equations. Zbl 1255.35042 Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian; Weiss, Daniel 6 2012 Linear energy-preserving integrators for Poisson systems. Zbl 1216.65175 Cohen, David; Hairer, Ernst 83 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 355 2010 Solving ordinary differential equations. I: Nonstiff problems. 2nd revised ed., 3rd corrected printing. Zbl 1185.65115 Hairer, Ernst; Nørsett, Syvert P.; Wanner, Gerhard 170 2010 Energy-preserving variant of collocation methods. Zbl 1432.65185 Hairer, E. 131 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 95 2010 Algebraic structures of B-series. Zbl 1201.65124 Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles 61 2010 Highly oscillatory problems. Zbl 1170.37002 29 2009 On energy conservation of the simplified Takahashi-Imada method. Zbl 1172.65067 Hairer, Ernst; McLachlan, Robert I.; Skeel, Robert D. 11 2009 Solving optimization-constrained differential equations with discontinuity points, with application to atmospheric chemistry. Zbl 1391.86007 Landry, Chantal; Caboussat, Alexandre; Hairer, Ernst 10 2009 Oscillation over long times in numerical Hamiltonian systems. Zbl 1180.37121 Hairer, Ernst; Lubich, Christian 10 2009 Long-time integration of non-stiff and oscillatory Hamiltonian systems. Zbl 1183.65169 Hairer, Ernst 1 2009 Nonlinear convergence analysis for the parareal algorithm. Zbl 1140.65336 Gander, Martin J.; Hairer, Ernst 82 2008 Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations. Zbl 1163.65066 Cohen, David; Hairer, Ernst; Lubich, Christian 68 2008 Computing breaking points in implicit delay differential equations. Zbl 1160.65041 Guglielmi, Nicola; Hairer, Ernst 40 2008 Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions. Zbl 1145.35087 Cohen, David; Hairer, Ernst; Lubich, Christian 37 2008 Achieving Brouwer’s law with implicit Runge-Kutta methods. Zbl 1148.65058 Hairer, E.; McLachlan, R. I.; Razakarivony, A. 29 2008 Spectral semi-discretisations of weakly non-linear wave equations over long times. Zbl 1156.35007 Hairer, E.; Lubich, C. 24 2008 Conjugate-symplecticity of linear multistep methods. Zbl 1174.65055 Hairer, Ernst 8 2008 Analysis by its history. Corr. 4th printing. Zbl 1139.26001 Hairer, Ernst; Wanner, Gerhard 8 2008 Numerical integrators based on modified differential equations. Zbl 1122.65059 Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles 20 2007 Modified differential equations. Zbl 1128.65053 Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles 1 2007 Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. 2nd ed. Zbl 1094.65125 Hairer, Ernst; Lubich, Christian; Wanner, Gerhard 1,457 2006 Report 14/2006: Geometric Numerical Integration (March 19th – March 25th, 2006). Zbl 1109.65301 14 2006 Symmetric linear multistep. Zbl 1149.65054 Hairer, Ernst 8 2006 Preprocessed discrete Moser-Veselov algorithm for the full dynamics of a rigid body. Zbl 1127.70002 Hairer, Ernst; Vilmart, Gilles 8 2006 Long-time energy conservation of numerical integrators. Zbl 1106.65334 Hairer, Ernst 6 2006 Numerical energy conservation for multi-frequency oscillatory differential equations. Zbl 1083.65117 Cohen, D.; Hairer, E.; Lubich, Ch. 35 2005 Explicit, time reversible, adaptive step size control. Zbl 1081.65117 Hairer, Ernst; Söderlind, Gustaf 20 2005 Important aspects of geometric numerical integration. Zbl 1203.65115 Hairer, Ernst 2 2005 Energy conservation with non-symplectic methods: examples and counter-examples. Zbl 1082.65132 Faou, Erwan; Hairer, Ernst; Pham, Truong-Linh 35 2004 Symmetric multistep methods over long times. Zbl 1060.65074 Hairer, Ernst; Lubich, Christian 27 2004 Geometric numerical integration illustrated by the Störmer-Verlet method. Zbl 1046.65110 Hairer, Ernst; Lubich, Christian; Wanner, Gerhard 145 2003 Modulated Fourier expansions of highly oscillatory differential equations. Zbl 1056.34005 Cohen, David; Hairer, Ernst; Lubich, Christian 33 2003 GniCodes –Matlab programs for geometric numerical integration. Zbl 1028.65136 Hairer, Ernst; Hairer, Martin 24 2003 Global modified Hamiltonian for constrained symplectic integrators. Zbl 1041.65102 Hairer, Ernst 4 2003 Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. Zbl 0994.65135 Hairer, Ernst; Lubich, Christian; Wanner, Gerhard 609 2002 Implementing Radau IIA methods for stiff delay differential equations. Zbl 0986.65069 Guglielmi, N.; Hairer, E. 49 2001 Geometric proofs of numerical stability for delay equations. Zbl 0976.65077 Guglielmi, Nicola; Hairer, Ernst 18 2001 Analysis by its history. Retranslation of the 2nd English edition of 1997. (L’analyse au fil de l’histoire. Retraduction du deuzième tirage de l’édition anglaise de 1997.) Zbl 0964.26003 Hairer, Ernst; Wanner, Gerhard 2 2001 Long-time energy conservation of numerical methods for oscillatory differential equations. Zbl 0988.65118 Hairer, Ernst; Lubich, Christian 117 2000 Symmetric projection methods for differential equations on manifolds. Zbl 0968.65108 Hairer, E. 28 2000 Energy conservation by Störmer-type numerical integrators. Zbl 0952.65053 Hairer, E.; Lubich, Ch. 8 2000 Asymptotic expansions and backward analysis for numerical integrators. Zbl 0942.65092 Hairer, Ernst; Lubich, Christian 6 2000 Order stars and stiff integrators. Zbl 0988.65059 Hairer, Ernst; Wanner, Gerhard 3 2000 Analysis by its history. Corr. 3rd printing. Zbl 0964.26002 Hairer, Ernst; Wanner, Gerhard 1 2000 Stiff differential equations solved by Radau methods. Zbl 0945.65080 Hairer, Ernst; Wanner, Gerhard 61 1999 Order stars and stability for delay differential equations. Zbl 0937.65079 Guglielmi, Nicola; Hairer, Ernst 29 1999 Backward error analysis for multistep methods. Zbl 0941.65077 Hairer, Ernst 16 1999 Invariant tori of dissipatively perturbed Hamiltonian systems under symplectic discretization. Zbl 1022.37042 Hairer, Ernst; Lubich, Christian 7 1999 Asymptotic error analysis of the adaptive Verlet method. Zbl 0924.65070 Cirilli, Stéphane; Hairer, Ernst; Leimkuhler, Benedict 6 1999 Order barriers for symplectic multi-value methods. Zbl 0902.65027 Hairer, E.; Leone, P. 10 1998 The life-span of backward error analysis for numerical integrators. Zbl 0874.65061 Hairer, E.; Lubich, Ch. 57 1997 Variable time step integration with symplectic methods. Zbl 0884.65073 Hairer, E. 34 1997 Order conditions for general two-step Runge-Kutta methods. Zbl 0890.65077 Hairer, Ernst; Wanner, Gerhard 23 1997 Reversible long-term integration with variable stepsizes. Zbl 0871.65075 Hairer, Ernst; Stoffer, Daniel 10 1997 Analysis by its history. Corr. 2nd print. Zbl 0964.26001 Hairer, Ernst; Wanner, Gerhard 2 1997 Solving ordinary differential equations. II: Stiff and differential-algebraic problems. 2nd rev. ed. Zbl 0859.65067 Hairer, Ernst; Wanner, Gerhard 1,435 1996 On error growth functions of Runge-Kutta methods. Zbl 0871.65071 Hairer, E.; Zennaro, M. 9 1996 On a generalization of a theorem of von Neumann. Zbl 0900.65238 Hairer, E.; Wanner, G. 4 1996 Accurate long-term integration of dynamical systems. Zbl 0837.65071 Calvo, M. P.; Hairer, E. 22 1995 Analysis by its history. Zbl 0842.26002 Hairer, E.; Wanner, G. 17 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. 5 1995 ...and 53 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 7,714 Authors 85 Wu, Xinyuan 81 Lubich, Christian 78 Hairer, Ernst 69 Simos, Theodore E. 65 Jackiewicz, Zdzislaw 62 Weiner, Rüdiger 61 Wang, Bin 61 Wang, Yushun 49 Tsitouras, Charalampos 44 Butcher, John C. 43 Ostermann, Alexander 41 Brugnano, Luigi 41 Ramos, Higinio 40 You, Xiong 39 D’Ambrosio, Raffaele 39 Montijano, Juan Ignacio 38 Abdi, Ali 38 Blanes, Sergio 38 Sanz-Serna, Jesús María 37 Casas, Fernando 37 Chartier, Philippe 37 Sandu, Adrian 35 González-Pinto, Severiano 34 Hojjati, Gholamreza 34 Murua, Ander 34 Rández, Luis 32 Calvo, Manuel 32 Fang, Yonglei 31 Auzinger, Winfried 31 Cai, Wenjun 31 Celledoni, Elena 31 McLachlan, Robert I. 31 Paternoster, Beatrice 31 Xiao, Aiguo 30 Iavernaro, Felice 30 Kulikov, Gennady Yur’evich 30 Owren, Brynjulf 29 Iserles, Arieh 29 Jiang, Yaolin 29 van der Houwen, Pieter J. 28 Gander, Martin Jakob 28 Li, Jiyong 27 Faou, Erwan 27 Hundsdorfer, Willem H. 27 Martín de Diego, David 27 Sommeijer, Ben P. 27 Wang, Wansheng 26 Van Daele, Marnix 26 Zhang, Chengjian 25 Burrage, Kevin 25 Franco, J. Méndez 25 Gong, Yuezheng 25 Leok, Melvin 25 Mehrmann, Volker 24 Conte, Dajana 24 Günther, Michael 24 Huang, Chengming 24 Podhaisky, Helmut 24 Shi, Wei 24 Vanden Berghe, Guido 23 Arnold, Martin 23 Hernandez-Abreu, Domingo 23 Liu, Mingzhu 23 Russo, Giovanni 23 Schmitt, Bernhard A. 23 Schratz, Katharina 23 Simeon, Bernd 23 Vigo-Aguiar, Jesus 22 Hong, Jialin 22 Ketcheson, David I. 22 Sun, Yajuan 22 Verwer, Jan G. 21 Boscarino, Sebastiano 21 Cong, Nguyen Huu 21 Ding, Xiaohua 21 Gan, Siqing 21 Karasözen, Bülent 21 Li, Shoufu 21 Senu, Norazak 21 Tian, Hongjiong 20 Hochbruck, Marlis 20 Izzo, Giuseppe 20 Koch, Othmar 20 Liu, Kai 20 Quispel, Gilles Reinout Willem 20 Shampine, Lawrence Fred 20 Vilmart, Gilles 19 Famelis, Ioannis Th. 19 Guglielmi, Nicola 19 Jator, Samuel N. 19 Jiang, Chaolong 19 Ober-Blöbaum, Sina 19 Strehmel, Karl 19 Wanner, Gerhard 19 Zhao, Jingjun 18 Akrivis, Georgios D. 18 Fu, Yayun 18 Hartmann, Stefan 18 Higueras, Inmaculada 18 Ismail, Fudziah Bt. ...and 7,614 more Authors all top 5 Cited in 553 Serials 617 Journal of Computational and Applied Mathematics 567 Applied Numerical Mathematics 482 Journal of Computational Physics 295 BIT 275 Applied Mathematics and Computation 196 Numerical Algorithms 194 Journal of Scientific Computing 185 Computers & Mathematics with Applications 170 Numerische Mathematik 160 Computer Methods in Applied Mechanics and Engineering 149 SIAM Journal on Scientific Computing 114 International Journal of Computer Mathematics 113 Mathematics of Computation 108 Computer Physics Communications 102 Mathematics and Computers in Simulation 98 SIAM Journal on Numerical Analysis 81 International Journal for Numerical Methods in Engineering 70 Applied Mathematics Letters 70 Communications in Nonlinear Science and Numerical Simulation 57 Foundations of Computational Mathematics 55 Multibody System Dynamics 52 Numerical Methods for Partial Differential Equations 50 Computing 50 Physica D 50 Advances in Computational Mathematics 44 Mathematical Methods in the Applied Sciences 42 Journal of Mathematical Chemistry 42 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 41 Computers and Fluids 41 Calcolo 41 Celestial Mechanics and Dynamical Astronomy 39 Computational and Applied Mathematics 38 Physics Letters. 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(English Edition) 10 Computational Methods in Applied Mathematics ...and 453 more Serials all top 5 Cited in 58 Fields 5,560 Numerical analysis (65-XX) 1,953 Ordinary differential equations (34-XX) 1,412 Partial differential equations (35-XX) 777 Dynamical systems and ergodic theory (37-XX) 662 Fluid mechanics (76-XX) 616 Mechanics of particles and systems (70-XX) 371 Probability theory and stochastic processes (60-XX) 355 Mechanics of deformable solids (74-XX) 295 Biology and other natural sciences (92-XX) 225 Systems theory; control (93-XX) 183 Statistical mechanics, structure of matter (82-XX) 177 Calculus of variations and optimal control; optimization (49-XX) 175 Integral equations (45-XX) 164 Computer science (68-XX) 162 Quantum theory (81-XX) 142 Optics, electromagnetic theory (78-XX) 114 Classical thermodynamics, heat transfer (80-XX) 112 Operations research, mathematical programming (90-XX) 95 Linear and multilinear algebra; matrix theory (15-XX) 89 Statistics (62-XX) 81 Approximations and expansions (41-XX) 80 Differential geometry (53-XX) 74 Operator theory (47-XX) 67 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 64 Information and communication theory, circuits (94-XX) 61 Geophysics (86-XX) 60 Real functions (26-XX) 48 Difference and functional equations (39-XX) 43 Combinatorics (05-XX) 36 Associative rings and algebras (16-XX) 33 Relativity and gravitational theory (83-XX) 31 Astronomy and astrophysics (85-XX) 28 Nonassociative rings and algebras (17-XX) 28 Global analysis, analysis on manifolds (58-XX) 24 History and biography (01-XX) 24 Topological groups, Lie groups (22-XX) 21 Harmonic analysis on Euclidean spaces (42-XX) 21 Integral transforms, operational calculus (44-XX) 17 Functional analysis (46-XX) 16 Special functions (33-XX) 13 General and overarching topics; collections (00-XX) 8 Geometry (51-XX) 7 Algebraic geometry (14-XX) 7 Manifolds and cell complexes (57-XX) 6 Functions of a complex variable (30-XX) 5 Number theory (11-XX) 4 Mathematical logic and foundations (03-XX) 4 Field theory and polynomials (12-XX) 3 Commutative algebra (13-XX) 3 Category theory; homological algebra (18-XX) 2 Measure and integration (28-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Abstract harmonic analysis (43-XX) 2 Mathematics education (97-XX) 1 Potential theory (31-XX) 1 Sequences, series, summability (40-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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