Ernst Hairer | Academic Influence

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Ernst Hairer

Mathematics

#1134

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#1914

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Measure Theory

#470

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#666

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Mathematics

Ernst Hairer's Degrees

PhD Mathematics University of Vienna

Why Is Ernst Hairer Influential?

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According to Wikipedia, Ernst Hairer is a professor of mathematics at the University of Geneva known for his work in numerical analysis. His PhD was completed at the University of Innsbruck. He is the father of the mathematician Martin Hairer, who won the Fields medal in 2014.

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Ernst Hairer's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems (2010) (5032)
Solving Ordinary Differential Equations I: Nonstiff Problems (2009) (4964)
Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations (2004) (3512)
Solving Ordinary Differential Equations II (2010) (2081)
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems (1993) (1255)
Geometric Numerical Integration (2022) (1060)
Solving Ordinary Differential Equations I (1991) (992)
Simulating Hamiltonian dynamics (2006) (822)
The numerical solution of differential-algebraic systems by Runge-Kutta methods (1989) (724)
Geometric numerical integration illustrated by the Störmer–Verlet method (2003) (555)
One-step and extrapolation methods for differential-algebraic systems (1987) (449)
Stiff and differential-algebraic problems (1991) (405)
Stiff differential equations solved by Radau methods (1999) (263)
Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations (2000) (241)
Order stars and stability theorems (1978) (202)
The life-span of backward error analysis for numerical integrators (1997) (194)
Backward analysis of numerical integrators and symplectic methods (1994) (188)
FAST NUMERICAL SOLUTION OF NONLINEAR VOLTERRA CONVOLUTION EQUATIONS (1985) (171)
Analysis by Its History (1996) (158)
Unconditionally stable methods for second order differential equations (1979) (158)
Energy-Preserving Variant of Collocation Methods 12 (2010) (157)
Nonlinear Convergence Analysis for the Parareal Algorithm (2008) (153)
On the Butcher group and general multi-value methods (1974) (144)
Energy-preserving variant of collocation methods 1 (2010) (139)
Implementing Radau IIA Methods for Stiff Delay Differential Equations (2001) (129)
Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations (2008) (123)
Linear energy-preserving integrators for Poisson systems (2011) (123)
Structure-Preserving Algorithms for Ordinary Differential Equations (2006) (121)
Solving Ordinary ,Differential Equations I, Nonstiff problems/E. Hairer, S. P. Norsett, G. Wanner, Second Revised Edition with 135 Figures, Vol.: 1 (2000) (114)
Variable time step integration with symplectic methods (1997) (113)
Implementation of Implicit Runge-Kutta Methods (1996) (111)
Numerical Treatment of Inverse Problems in Differential and Integral Equations: Proceedings of an International Workshop, Heidelberg, Fed. Rep. of Germany, August 30 - September 3, 1982 (2012) (107)
A theory for Nyström methods (1975) (105)
Examples of Stiff Equations (1996) (103)
Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations (1988) (103)
Numerical methods for evolutionary differential equations (2010) (101)
Algebraic Structures of B-series (2010) (89)
Energy Conservation with Non-Symplectic Methods: Examples and Counter-Examples (2004) (87)
Computing breaking points in implicit delay differential equations (2008) (83)
Introduction to Analysis of the Infinite (2008) (81)
Algebraically Stable and Implementable Runge-Kutta Methods of High Order (1981) (81)
A Runge-Kutta Method of Order 10 (1978) (78)
Numerical Energy Conservation for Multi-Frequency Oscillatory Differential Equations (2005) (74)
Modulated Fourier Expansions of Highly Oscillatory Differential Equations (2003) (72)
Highly Oscillatory Problems (2009) (70)
Symmetric Projection Methods for Differential Equations on Manifolds (2000) (70)
Order conditions for numerical methods for partitioned ordinary differential equations (1981) (70)
Half-explicit Runge-Kutta methods for differential-algebraic systems of index 2 (1993) (69)
Achieving Brouwer’s law with implicit Runge–Kutta methods (2008) (66)
Long-Time Analysis of Nonlinearly Perturbed Wave Equations Via Modulated Fourier Expansions (2008) (64)
Energy-diminishing integration of gradient systems (2014) (64)
Accurate long-term integration of dynamical systems (1995) (63)
Symmetric multistep methods over long times (2004) (63)
Runge-Kutta theory for Volterra integral equations of the second kind (1982) (61)
Unconditionally stable explicit methods for parabolic equations (1980) (59)
Fast numerical solution of weakly singular Volterra integral equations (1988) (59)
Numerical integrators based on modified differential equations (2007) (59)
Geometric Integration of Ordinary Differential Equations on Manifolds (2001) (59)
Explicit, Time Reversible, Adaptive Step Size Control (2005) (58)
On the stability of semi-implicit methods for ordinary differential equations (1982) (56)
Order stars and stability for delay differential equations (1999) (49)
A One-step Method of Order 10 for y″=f(x,y) (1982) (46)
Reversible Long-Term Integration with Variable Stepsizes (1997) (44)
A substitution law for B-series vector fields (2005) (43)
Long-Term Stability of Multi-Value Methods for Ordinary Differential Equations (2014) (43)
Equilibria of Runge-Kutta methods (1990) (42)
Order of Convergence of One-Step Methods for Volterra Integral Equations of the Second Kind (1983) (42)
Preprocessed discrete Moser-Veselov algorithm for the full dynamics of a rigid body (2006) (42)
Order Conditions for General Two-Step Runge--Kutta Methods (1997) (42)
Asymptotic expansions of the global error of fixed-stepsize methods (1984) (41)
Multistep-multistage-multiderivative methods for ordinary differential equations (1973) (40)
The role of symplectic integrators in optimal control (2009) (40)
Spectral Semi-discretisations of Weakly Non-linear Wave Equations over Long Times (2008) (39)
Symmetric multistep methods for charged-particle dynamics (2017) (38)
Analysis for parareal algorithms applied to Hamiltonian differential equations (2014) (38)
Rosenbrock-Type Methods (1996) (37)
Energy behaviour of the Boris method for charged-particle dynamics (2018) (36)
A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field (2019) (34)
Dense output for extrapolation methods (1990) (34)
On conjugate symplecticity of B-series integrators (2013) (32)
Long-term analysis of the Störmer–Verlet method for Hamiltonian systems with a solution-dependent high frequency (2016) (31)
GniCodes - Matlab programs for geometric numerical integration (2003) (31)
Backward error analysis for multistep methods (1999) (31)
Classification of Hidden Dynamics in Discontinuous Dynamical Systems (2015) (30)
Order barriers for symplectic multi-value methods (1998) (28)
Highest possible order of algebraically stable diagonally implicit runge-kutta methods (1980) (28)
Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field (2020) (28)
G-symplecticity implies conjugate-symplecticity of the underlying one-step method (2013) (28)
Extrapolation at stiff differential equations (1988) (26)
CONJUGATE-SYMPLECTICITY OF LINEAR MULTISTEP METHODS (2008) (26)
On the Energy Distribution in Fermi–Pasta–Ulam Lattices (2012) (26)
ON ENERGY CONSERVATION OF THE SIMPLIFIED TAKAHASHI-IMADA METHOD. (2009) (25)
Geometric proofs of numerical stability for delay equations (2001) (25)
On the Instability of the BDF Formulas (1983) (23)
Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions (2014) (23)
Solving Optimization-Constrained Differential Equations with Discontinuity Points, with Application to Atmospheric Chemistry (2009) (22)
Oscillations over long times in numerical Hamiltonian systems (2009) (20)
Acta Numerica 2003: Geometric numerical integration illustrated by the Störmer–Verlet method (2003) (20)
Long-time energy conservation of numerical integrators (2006) (19)
Invariant tori of dissipatively perturbed Hamiltonian systems under symplectic discretization (1999) (19)
Energy Separation in Oscillatory Hamiltonian Systems without any Non-resonance Condition (2012) (19)
Asymptotic Error Analysis of the Adaptive Verlet Method (1999) (19)
Global modified Hamiltonian for constrained symplectic integrators (2003) (19)
The non-existence of symplectic multi-derivative Runge-Kutta methods (1994) (18)
Implicit Runge-Kutta methods for higher index differential-algebraic systems (1993) (18)
On the Stability of Volterra–Runge–Kutta Methods (1984) (18)
Modulated Fourier Expansions for Continuous and Discrete Oscillatory Systems (2012) (16)
Energy conservation by Stoermer-type numerical integrators (2000) (16)
Characterization of non-linearly stable implicit Runge-Kutta methods (1982) (16)
On the order of iterated defect correction (1978) (15)
Solving Differential Equations on Manifolds (2011) (15)
Numerical approaches for state-dependent neutral delay equations with discontinuities (2014) (15)
Singular Perturbation Problems and Differential Algebraic Equations (1991) (14)
Symmetric linear multistep methods (2006) (14)
Important Aspects of Geometric Numerical Integration (2005) (14)
DYNAMICS, NUMERICAL ANALYSIS, AND SOME GEOMETRY (2017) (14)
Numerical methods for singular nonlinear integro-differential equations (1987) (14)
Current Challenges in Stability Issues for Numerical Differential Equations (2013) (14)
Asymptotic expansions and backward analysis for numerical integrators (2000) (14)
Asymptotic Expansions for Regularized State-Dependent Neutral Delay Equations (2012) (13)
Order stars and stiff integrators (2000) (13)
Symmetric multistep methods for constrained Hamiltonian systems (2013) (12)
The equivalence ofB-stability andA-stability (1984) (12)
Metastable Energy Strata in Weakly Nonlinear Wave Equations (2012) (12)
Further reduction in the number of independent order conditions for sympletic, explicit partitioned Runge-Kutta and Runge-Kutta-Nystro¨m methods (1995) (11)
Runge-Kutta methods for differential-algebraic equations (1989) (11)
Numerical Stability in the Presence of Variable Coefficients (2016) (11)
Symplectic Runge-Kutta methods with real eigenvalues (1994) (10)
A necessary condition forBSI-stability (1985) (10)
Runge-Kutta and Extrapolation Methods (1987) (10)
On error growth functions of Runge-Kutta methods (1996) (10)
Constructive characterization ofA-stable approximations to exp(z) and its connection with algebraically stable Runge-Kutta methods (1982) (10)
Long-term analysis of semilinear wave equations with slowly varying wave speed (2016) (10)
Hamiltonian Perturbation Theory and Symplectic Integrators (2006) (9)
Stiff Problems — One-Step Methods (1991) (9)
A- andB-stability for Runge-Kutta methods-characterizations and equivalence (1986) (9)
A Theory for Nystr6m Methods (1976) (9)
Nonlinear stability ofRAT, an explicit rational Runge-Kutta method (1979) (9)
Long-Term Stability of Symmetric Partitioned Linear Multistep Methods (2014) (9)
Symmetrized half-explicit methods for constrained mechanical systems (1993) (9)
Modified differential equations (2007) (8)
AMF-type W-methods for Parabolic Problems with Mixed Derivatives (2018) (8)
Solutions leaving a codimension-2 sliding (2016) (8)
Long-term control of oscillations in differential equations (2013) (7)
WhenI-stability impliesA-stability (1978) (7)
PDE-W-methods for parabolic problems with mixed derivatives (2018) (7)
Linear multistep method (2010) (7)
Large-stepsize integrators for charged-particle dynamics over multiple time scales (2021) (7)
Error of rosenbrock methods for stiff problems studied via differential algebraic equations (1989) (7)
Classical Mathematical Theory (1987) (7)
Algebraic Stability of General Linear Methods (1996) (7)
THE EQUIVALENCE OF B-STABILITY A N D A-STABILITY (6)
Regularization of Neutral Delay Differential Equations with Several Delays (2013) (6)
Stiff delay equations (2007) (6)
Challenges in Geometric Numerical Integration (2014) (6)
Convergence in ℓ2 and ℓ∞ Norm of One-Stage AMF-W-Methods for Parabolic Problems (2020) (5)
Reducing round-off errors in symmetric multistep methods (2014) (5)
Solutions leaving a codimension-$$\varvec{2}$$2 sliding (2017) (5)
Construction of Implicit Runge-Kutta Methods (1996) (4)
GEOMETRIC INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS (2001) (4)
An efficient algorithm for solving piecewise-smooth dynamical systems (2021) (4)
Symplectic integrators in sub-Riemannian geometry: the Martinet case (2006) (4)
Symplectic Methods for Constrained Hamiltonian Systems (1996) (4)
Long‐time Integration of Non‐Stiff and Oscillatory Hamiltonian Systems (2009) (4)
Description of differential-algebraic problems (1989) (3)
Conjugate symplectic B-series (2012) (3)
Path-regularization of linear neutral delay differential equations with several delays (2016) (3)
Multistep Methods and General Linear Methods (1987) (3)
Symplectic Integration of Hamiltonian Systems (2006) (3)
BIT Numerical Mathematics: Editorial (2005) (3)
Corrigendum to: “Symplectic integrators for the Ablowitz-Ladik discrete nonlinear Schrödinger equation: implementation issues”. [Phys. Lett. A 259 (1999) 140-151] (2000) (3)
Power boundedness in the maximum norm of stability matrices for ADI methods (2021) (3)
On a Generalization of a Theorem of von Neumann (1996) (3)
Structure-Preserving Implementation (2006) (3)
Some properties of symplectic Runge-Kutta methods (2000) (3)
Banded, stable, skew-symmetric differentiation matrices of high order (2016) (2)
Rational Approximations to the Exponential Function with Two Complex Conjugate Interpolation Points (1985) (2)
Book Review: Numerical methods for evolutionary differential equations (2010) (2)
Dense output for the GBS extrapolation method (1992) (2)
Stability of Multistep Methods (1996) (2)
Backward Error Analysis and Structure Preservation (2006) (2)
Highly Oscillatory Differential Equations (2002) (2)
Multistep Methods for Index 2 DAE (1996) (2)
On conjectures of Stenger in the theory of orthogonal polynomials (2019) (2)
Sti ! di ! erential equations solved by Radau methods (2018) (2)
Order conditions of Runge-Kutta methods for index 2 systems (1989) (2)
Existence and Uniqueness of IRK Solutions (1996) (2)
A note onD-stability (1984) (2)
Examples of differential-algebraic systems and their solution (1989) (1)
Important aspects of geometric numerical integration (2005) (1)
Convergence for index 3 problems (1989) (1)
Convergence for index 1 problems (1989) (1)
Symmetric Integration and Reversibility (2006) (1)
Multistep Methods for Stiff Problems (1991) (1)
Study of discontinuous differential equations close to the intersection of two discontinuity surfaces (2016) (1)
Numerical solution of ordinary differential equations (2010) (1)
Stability Analysis for Explicit RK Methods (1996) (1)
Foundations of Computational Mathematics, Santander 2005: Long-time Energy Conservation (2006) (1)
Order Conditions, Trees and B-Series (2006) (1)
Local error estimation (1989) (1)
Computation of Multibody Mechanisms (1996) (1)
Runge-Kutta Methods for Index 2 DAE (1996) (1)
Dynamics of Multistep Methods (2006) (1)
Convergence for index 2 problems (1989) (1)
Stability Function of Implicit RK-Methods (1996) (0)
One-Leg Methods and G-Stability (1996) (0)
Sliding modes of high codimension in piecewise-smooth dynamical systems (2023) (0)
Conservation of First Integrals and Methods on Manifolds (2006) (0)
Numerical Energy Preservation of General Hamiltonian Systems (2010) (0)
High order PDE-convergence of AMF-W methods for 2D-linear parabolic problems (2022) (0)
The Method of Lie Series for Differential Equations and Its Extensions. (1973) (0)
Energy Separation in Oscillatory Hamiltonian Systems without any Non-resonance Condition (2013) (0)
Non-Canonical Hamiltonian Systems (2006) (0)
Book Review: Numerical Methods for Delay Differential Equations. by Alfredo Bellen and Marino Zennaro (2004) (0)
Order Conditions for Index 2 DAE (1996) (0)
Epsilon Expansions for Exact and RK Solutions (1996) (0)
Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field (2020) (0)
Oscillatory Differential Equations with Varying High Frequencies (2006) (0)
Dissipatively Perturbed Hamiltonian and Reversible Systems (2006) (0)
Leapfrog methods for relativistic charged-particle dynamics (2023) (0)
The Index and Various Examples (1996) (0)
Book Review: Simulating Hamiltonian dynamics (2006) (0)
Further Topics in Structure Preservation (2002) (0)
High-order rigid body integrators based on modified differential equations (2006) (0)
On conjectures of Stenger in the theory of orthogonal polynomials (2019) (0)
A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field (2020) (0)
Long-time numerical energy preservation for oscillatory differential equations (2015) (0)
Calculus in Several Variables (2008) (0)
Order Stars on Riemann Surfaces (1996) (0)
Positive Quadrature Formulas and B-Stable RK-Methods (1996) (0)
Energy behaviour of the Boris method for charged-particle dynamics (2018) (0)
G-symplecticity implies conjugate-symplecticity of the underlying one-step method (2013) (0)
Oscillatory Differential Equations with Constant High Frequencies (2006) (0)
Banded, skew-symmetric differentiation matrices of high order (2017) (0)
Solving Index 1 Problems (1996) (0)
Half-Explicit Methods for Index 2 Systems (1996) (0)
Index Reduction Methods (1996) (0)
Symmetric multistep methods for constrained Hamiltonian systems (2013) (0)
Composing and substituting S-series and B-series of integrators and vector fields (2008) (0)
Highly Oscillatory Problems: Preface (2009) (0)
Solution of nonlinear systems by simplified Newton (1989) (0)
Foundations of Classical Analysis (2008) (0)
Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions (2014) (0)
Experiments with Multistep Codes (1996) (0)
Convergence for Linear Problems (1996) (0)
An efficient algorithm for solving piecewise-smooth dynamical systems (2021) (0)
Long-term analysis of the Störmer–Verlet method for Hamiltonian systems with a solution-dependent high frequency (2015) (0)
SYMMETRIC LINEAR MULTISTEP METHODS (cid:1) (2006) (0)
SYMMETRIC LINEAR MULTISTEP METHODS (cid:1) (2006) (0)
Convergence for Nonlinear Problems (1996) (0)
Generalized Multistep Methods (1996) (0)
Long-Term Stability of Multi-Value Methods for Ordinary Differential Equations (2013) (0)
On the Energy Distribution in Fermi–Pasta–Ulam Lattices (2012) (0)
PDE-W-methods for parabolic problems with mixed derivatives (2017) (0)
Examples and Numerical Experiments (2006) (0)
Regularization of Neutral Delay Differential Equations with Several Delays (2013) (0)
“Nearly” A-Stable Multistep Methods (1996) (0)
Reversible Perturbation Theory and Symmetric Integrators (2006) (0)
Diagonally Implicit RK Methods (1996) (0)
B-Stability and Contractivity (1996) (0)
Contractivity for Linear Problems (1996) (0)
Numerical Stability in the Presence of Variable Coefficients (2015) (0)
The Solution of Differential Equations by the Method of Lie Series and Its Generalizations. (1972) (0)

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