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## Lubich, Christian

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 Author ID: lubich.christian Published as: Lubich, C.; Lubich, Ch.; Lubich, Christian Homepage: https://na.uni-tuebingen.de/~lubich/ External Links: MGP · Wikidata · ORCID · dblp · GND
 Documents Indexed: 165 Publications since 1982, including 5 Books
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#### Co-Authors

 30 single-authored 46 Hairer, Ernst 10 Guglielmi, Nicola 10 Hochbruck, Marlis 9 Gauckler, Ludwig J. 9 Kovács, Balázs 7 Ostermann, Alexander 6 Li, Buyang 4 Banjai, Lehel 4 Faou, Erwan 4 Jahnke, Tobias 4 Koch, Othmar 4 Roche, Michel 4 Schädle, Achim 4 Wanner, Gerhard 3 Akrivis, Georgios D. 3 Cohen, David W. 3 Eggermont, Paul P. B. 3 López-Fernández, María 3 Mansour, Dhia 3 Vandereycken, Bart 3 Walach, Hanna 2 Andreotti, Eleonora 2 Ceruti, Gianluca 2 Edelmann, Dominik 2 Einkemmer, Lukas 2 Engstler, Christian 2 Iserles, Arieh 2 Kressner, Daniel 2 Lorenz, Katina 2 Oseledets, Ivan V. 2 Palencia, Cesar 2 Schlichte, M. 2 Weiss, Daniel A. 1 Bader, Georges 1 Bartels, Sören 1 Cohen, David A. 1 Cohen, David Mordecai 1 Cohen, Dror 1 Console, Paola 1 Conte, Dajana 1 Cuesta, Eduardo 1 Dziuk, Gerhard 1 Feischl, Michael 1 Gradinaru, Vasile 1 Holden, Helge 1 in ’t Hout, Karel J. 1 Kieri, Emil 1 Kunstmann, Peer Christian 1 Makridakis, Charalambos G. 1 Mehrmann, Volker 1 Melenk, Jens Markus 1 Nevanlinna, Olavi 1 Nipp, Kaspar 1 Nonnenmacher, Achim 1 Nørsett, Syvert Paul 1 Power Guerra, Christian Andreas 1 Prohl, Andreas 1 Richter, Ronny 1 Risebro, Nils Henrik 1 Rohwedder, Thorsten 1 Sayas, Francisco-Javier 1 Schneider R. 1 Schneider, Reinhold 1 Sloan, Ian Hugh 1 Stoffer, Daniel 1 Thomée, Vidar 1 van Dorsselaer, Jos L. M. 1 Venkataraman, Chandrasekhar 1 Wang, Bin
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#### Serials

 31 Numerische Mathematik 18 BIT 15 Mathematics of Computation 14 SIAM Journal on Numerical Analysis 11 IMA Journal of Numerical Analysis 8 SIAM Journal on Scientific Computing 7 SIAM Journal on Matrix Analysis and Applications 6 Applied Numerical Mathematics 5 Foundations of Computational Mathematics 3 Communications in Partial Differential Equations 3 Oberwolfach Reports 3 Springer Series in Computational Mathematics 2 Archive for Rational Mechanics and Analysis 2 Computing 2 IMPACT of Computing in Science and Engineering 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Classical and Quantum Gravity 1 Communications in Mathematical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Journal of Computational and Applied Mathematics 1 Mathematics and Computers in Simulation 1 Journal of Integral Equations 1 SIAM Journal on Scientific and Statistical Computing 1 Internationale Mathematische Nachrichten 1 Journal of Integral Equations and Applications 1 Linear Algebra and its Applications 1 SIAM Journal on Mathematical Analysis 1 Discrete and Continuous Dynamical Systems 1 Interfaces and Free Boundaries 1 AMRX. Applied Mathematics Research eXpress 1 Multiscale Modeling & Simulation 1 Acta Numerica 1 Lecture Notes in Mathematics 1 Forum of Mathematics, Sigma 1 Zurich Lectures in Advanced Mathematics 1 SMAI Journal of Computational Mathematics
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#### Fields

 148 Numerical analysis (65-XX) 52 Partial differential equations (35-XX) 48 Ordinary differential equations (34-XX) 27 Dynamical systems and ergodic theory (37-XX) 23 Integral equations (45-XX) 17 Linear and multilinear algebra; matrix theory (15-XX) 15 Mechanics of particles and systems (70-XX) 12 Quantum theory (81-XX) 5 Integral transforms, operational calculus (44-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Optics, electromagnetic theory (78-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Real functions (26-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Operations research, mathematical programming (90-XX) 2 Systems theory; control (93-XX) 1 Functions of a complex variable (30-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Differential geometry (53-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Fluid mechanics (76-XX) 1 Relativity and gravitational theory (83-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH

153 Publications have been cited 5,881 times in 3,520 Documents Cited by Year
Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. 2nd ed. Zbl 1094.65125
Hairer, Ernst; Lubich, Christian; Wanner, Gerhard
2006
Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. Zbl 0994.65135
Hairer, Ernst; Lubich, Christian; Wanner, Gerhard
2002
Discretized fractional calculus. Zbl 0624.65015
Lubich, Ch.
1986
Convolution quadrature and discretized operational calculus. I. Zbl 0637.65016
Lubich, C.
1988
The numerical solution of differential-algebraic systems by Runge-Kutta methods. Zbl 0683.65050
Hairer, Ernst; Lubich, Christian; Roche, Michel
1989
On Krylov subspace approximations to the matrix exponential operator. Zbl 0888.65032
Hochbruck, Marlis; Lubich, Christian
1997
Exponential integrators for large systems of differential equations. Zbl 0912.65058
Hochbruck, Marlis; Lubich, Christian
1998
Convolution quadrature and discretized operational calculus. II. Zbl 0643.65094
Lubich, C.
1988
Convolution quadrature time discretization of fractional diffusion-wave equations. Zbl 1090.65147
Cuesta, Eduardo; Lubich, Christian; Palencia, Cesar
2006
On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations. Zbl 1198.65186
Lubich, Christian
2008
A Gautschi-type method for oscillatory second-order differential equations. Zbl 0937.65077
Hochbruck, Marlis; Lubich, Christian
1999
Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term. Zbl 0852.65138
Lubich, Ch.; Sloan, I. H.; Thomée, V.
1996
Fractional linear multistep methods for Abel-Volterra integral equations of the second kind. Zbl 0584.65090
Lubich, Ch.
1985
From quantum to classical molecular dynamics: Reduced models and numerical analysis. Zbl 1160.81001
Lubich, Christian
2008
On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations. Zbl 0795.65063
Lubich, Ch.
1994
Geometric numerical integration illustrated by the Störmer-Verlet method. Zbl 1046.65110
Hairer, Ernst; Lubich, Christian; Wanner, Gerhard
2003
Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations. Zbl 0657.65093
Hairer, E.; Lubich, Ch.; Roche, M.
1988
Error bounds for exponential operator splittings. Zbl 0972.65061
Jahnke, Tobias; Lubich, Christian
2000
Long-time energy conservation of numerical methods for oscillatory differential equations. Zbl 0988.65118
Hairer, Ernst; Lubich, Christian
2000
Fast convolution for nonreflecting boundary conditions. Zbl 1013.65113
Lubich, Christian; Schädle, Achim
2002
Fast and oblivious convolution quadrature. Zbl 1111.65114
Schädle, Achim; López-Fernández, María; Lubich, Christian
2006
Lubich, Christian
2004
Runge-Kutta methods for parabolic equations and convolution quadrature. Zbl 0795.65062
Lubich, Ch.; Ostermann, A.
1993
On the stability of linear multistep methods for Volterra convolution equations. Zbl 0543.65095
Lubich, Ch.
1983
Runge-Kutta theory for Volterra and Abel integral equations of the second kind. Zbl 0538.65091
Lubich, Ch.
1983
Fast numerical solution of nonlinear Volterra convolution equations. Zbl 0581.65095
Hairer, E.; Lubich, Ch.; Schlichte, M.
1985
Dynamical low-rank approximation. Zbl 1145.65031
Koch, Othmar; Lubich, Christian
2008
Multi-grid dynamic iteration for parabolic equations. Zbl 0623.65125
Lubich, Ch.; Ostermann, A.
1987
The life-span of backward error analysis for numerical integrators. Zbl 0874.65061
Hairer, E.; Lubich, Ch.
1997
Linearly implicit time discretization of nonlinear parabolic equations. Zbl 0834.65092
Lubich, Ch.; Ostermann, A.
1995
Runge-Kutta approximation of quasi-linear parabolic equations. Zbl 0832.65104
Lubich, Christian; Ostermann, Alexander
1995
On resolvent conditions and stability estimates. Zbl 0731.65043
Lubich, Christian; Nevanlinna, Olavi
1991
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
Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations. Zbl 1163.65066
Cohen, David; Hairer, Ernst; Lubich, Christian
2008
Runge-Kutta convolution quadrature for operators arising in wave propagation. Zbl 1227.65027
Banjai, Lehel; Lubich, Christian; Melenk, Jens Markus
2011
On the stability of semi-implicit methods for ordinary differential equations. Zbl 0489.65046
Hairer, E.; Bader, G.; Lubich, Ch.
1982
A stability analysis of convolution quadratures for Abel-Volterra integral equations. Zbl 0587.65090
Lubich, Ch.
1986
Dynamical approximation by hierarchical Tucker and tensor-train tensors. Zbl 1391.15087
Lubich, Christian; Rohwedder, Thorsten; Schneider, Reinhold; Vandereycken, Bart
2013
Dynamical tensor approximation. Zbl 1214.15017
Koch, Othmar; Lubich, Christian
2010
Time discretization of parabolic boundary integral equations. Zbl 0795.65061
Lubich, Ch.; Schneider R.
1992
Error of Rosenbrock methods for stiff problems studied via differential algebraic equations. Zbl 0674.65039
Hairer, E.; Lubich, Ch.; Roche, M.
1989
Adaptive, fast, and oblivious convolution in evolution equations with memory. Zbl 1160.65356
López-Fernández, María; Lubich, Christian; Schädle, Achim
2008
Operator splitting for partial differential equations with Burgers nonlinearity. Zbl 1260.35184
Holden, Helge; Lubich, Christian; Risebro, Nils Henrik
2013
On the convergence of multistep methods for nonlinear stiff differential equations. Zbl 0729.65055
Lubich, C.
1991
A projector-splitting integrator for dynamical low-rank approximation. Zbl 1314.65095
Lubich, Christian; Oseledets, Ivan
2014
Backward difference time discretization of parabolic differential equations on evolving surfaces. Zbl 1401.65108
Lubich, Christian; Mansour, Dhia; Venkataraman, Chandrasekhar
2013
Fast numerical solution of weakly singular Volterra integral equations. Zbl 0654.65091
Hairer, E.; Lubich, Ch.; Schlichte, M.
1988
Asymptotic expansions of the global error of fixed-stepsize methods. Zbl 0571.65066
Hairer, E.; Lubich, C.
1984
Numerical integrators for highly oscillatory Hamiltonian systems: a review. Zbl 1367.65191
Cohen, David; Jahnke, Tobias; Lorenz, Katina; Lubich, Christian
2006
Numerical energy conservation for multi-frequency oscillatory differential equations. Zbl 1083.65117
Cohen, D.; Hairer, E.; Lubich, Ch.
2005
Exponential integrators for quantum-classical molecular dynamics. Zbl 0985.81002
Hochbruck, Marlis; Lubich, Christian
1999
Extrapolation integrators for constrained multibody systems. Zbl 0742.70011
Lubich, Ch.
1991
Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations. Zbl 1361.65053
Akrivis, Georgios; Li, Buyang; Lubich, Christian
2017
A-stable time discretizations preserve maximal parabolic regularity. Zbl 1355.65122
Kovács, Balázs; Li, Buyang; Lubich, Christian
2016
Time integration of tensor trains. Zbl 1312.65114
Lubich, Christian; Oseledets, Ivan V.; Vandereycken, Bart
2015
An error analysis of Runge-Kutta convolution quadrature. Zbl 1228.65245
Banjai, Lehel; Lubich, Christian
2011
Splitting integrators for nonlinear Schrödinger equations over long times. Zbl 1189.65301
Gauckler, Ludwig; Lubich, Christian
2010
Computing semiclassical quantum dynamics with Hagedorn wavepackets. Zbl 1194.81096
Faou, Erwan; Gradinaru, Vasile; Lubich, Christian
2009
Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions. Zbl 1145.35087
Cohen, David; Hairer, Ernst; Lubich, Christian
2008
Energy-diminishing integration of gradient systems. Zbl 1321.65115
Hairer, Ernst; Lubich, Christian
2014
Integration of stiff mechanical systems by Runge-Kutta methods. Zbl 0784.70002
Lubich, Ch.
1993
Symmetric multistep methods over long times. Zbl 1060.65074
Hairer, Ernst; Lubich, Christian
2004
Runge-Kutta time discretization of reaction-diffusion and Navier-Stokes equations: Nonsmooth-data error estimates and applications to long-time behaviour. Zbl 0872.65090
Lubich, Christian; Ostermann, Alexander
1996
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
Runge-Kutta theory for Volterra integrodifferential equations. Zbl 0491.65064
Lubich, Ch.
1982
Fully implicit, linearly implicit and implicit-explicit backward difference formulae for quasi-linear parabolic equations. Zbl 1334.65124
Akrivis, Georgios; Lubich, Christian
2015
On Magnus integrators for time-dependent Schrödinger equations. Zbl 1049.65064
Hochbruck, Marlis; Lubich, Christian
2003
Nonlinear Schrödinger equations and their spectral semi-discretizations over long times. Zbl 1194.37121
Gauckler, Ludwig; Lubich, Christian
2010
Multirate extrapolation methods for differential equations with different time scales. Zbl 0891.65083
Engstler, Ch.; Lubich, Ch.
1997
Stable numerical coupling of exterior and interior problems for the wave equation. Zbl 1314.65122
Banjai, Lehel; Lubich, Christian; Sayas, Francisco-Javier
2015
Discretized dynamical low-rank approximation in the presence of small singular values. Zbl 1336.65119
Kieri, Emil; Lubich, Christian; Walach, Hanna
2016
Low-rank dynamics for computing extremal points of real pseudospectra. Zbl 1272.65032
Guglielmi, Nicola; Lubich, Christian
2013
Differential equations for roaming pseudospectra: paths to extremal points and boundary tracking. Zbl 1232.15009
Guglielmi, Nicola; Lubich, Christian
2011
Dynamical low-rank approximation: Applications and numerical experiments. Zbl 1162.65335
Nonnenmacher, Achim; Lubich, Christian
2008
Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus. Zbl 1274.35357
Faou, Erwan; Gauckler, Ludwig; Lubich, Christian
2013
Modulated Fourier expansions of highly oscillatory differential equations. Zbl 1056.34005
Cohen, David; Hairer, Ernst; Lubich, Christian
2003
Fractional linear multistep methods for Abel Volterra integral equations of the first kind. Zbl 0624.65137
Lubich, Ch.
1987
Spectral semi-discretisations of weakly non-linear wave equations over long times. Zbl 1156.35007
Hairer, E.; Lubich, C.
2008
Periodic orbits of delay differential equations under discretization. Zbl 0904.65066
in’t Hout, Karel J.; Lubich, Christian
1998
Interior estimates for time discretizations of parabolic equations. Zbl 0841.65080
Lubich, Christian; Ostermann, Alexander
1995
Low rank differential equations for Hamiltonian matrix nearness problems. Zbl 1312.65070
Guglielmi, Nicola; Kressner, Daniel; Lubich, Christian
2015
Runge-Kutta time discretization of parabolic differential equations on evolving surfaces. Zbl 1247.65124
Dziuk, G.; Lubich, Ch.; Mansour, D.
2012
Fast Runge-Kutta approximation of inhomogeneous parabolic equations. Zbl 1082.65095
López-Fernández, María; Lubich, Christian; Palencia, Cesar; Schädle, Achim
2005
On variational approximations in quantum molecular dynamics. Zbl 1059.81188
Lubich, Christian
2005
On convolution quadrature and Hille-Phillips operational calculus. Zbl 0747.65013
Lubich, C.
1992
Rosenbrock methods for differential-algebraic systems with solution- dependent singular matrix multiplying the derivative. Zbl 0692.65038
Lubich, Ch.; Roche, M.
1990
h$${}^ 2$$-extrapolation methods for differential-algebraic systems of index 2. Zbl 0714.65067
Lubich, Ch.
1989
Time integration in the multiconfiguration time-dependent Hartree method of molecular quantum dynamics. Zbl 1331.35290
Lubich, Christian
2015
Numerical analysis of parabolic problems with dynamic boundary conditions. Zbl 1433.65216
Kovács, Balázs; Lubich, Christian
2017
Regularity of the multi-configuration time-dependent Hartree approximation in quantum molecular dynamics. Zbl 1135.81380
Koch, Othmar; Lubich, Christian
2007
Uniform error estimates of operational quadrature methods for nonlinear convolution equations on the half-line. Zbl 0709.65119
Eggermont, P. P. B.; Lubich, Ch.
1991
Energy behaviour of the Boris method for charged-particle dynamics. Zbl 1404.65309
Hairer, Ernst; Lubich, Christian
2018
On the nearest singular matrix pencil. Zbl 1371.15015
Guglielmi, Nicola; Lubich, Christian; Mehrmann, Volker
2017
On the energy distribution in Fermi-Pasta-Ulam lattices. Zbl 1283.70011
Hairer, Ernst; Lubich, Christian
2012
Numerical integrators for quantum dynamics close to the adiabatic limit. Zbl 1029.65069
Jahnke, Tobias; Lubich, Christian
2003
Linearly implicit extrapolation methods for differential-algebraic systems. Zbl 0669.65057
Lubich, C.
1989
Extrapolation at stiff differential equations. Zbl 0643.65034
Hairer, E.; Lubich, C.
1988
On the stability of Volterra-Runge-Kutta methods. Zbl 0532.65086
Hairer, E.; Lubich, Ch.
1984
Time integration of rank-constrained Tucker tensors. Zbl 1407.37113
Lubich, Christian; Vandereycken, Bart; Walach, Hanna
2018
Long-term analysis of the Störmer-Verlet method for Hamiltonian systems with a solution-dependent high frequency. Zbl 1408.65100
Hairer, Ernst; Lubich, Christian
2016
Long-term 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
A convergent evolving finite element algorithm for mean curvature flow of closed surfaces. Zbl 1427.65250
Kovács, Balázs; Li, Buyang; Lubich, Christian
2019
A quasi-conservative Dynamical Low-rank algorithm for the Vlasov equation. Zbl 1428.82058
Einkemmer, Lukas; Lubich, Christian
2019
Constrained graph partitioning via matrix differential equations. Zbl 1407.05187
Andreotti, Eleonora; Edelmann, Dominik; Guglielmi, Nicola; Lubich, Christian
2019
Energy behaviour of the Boris method for charged-particle dynamics. Zbl 1404.65309
Hairer, Ernst; Lubich, Christian
2018
Time integration of rank-constrained Tucker tensors. Zbl 1407.37113
Lubich, Christian; Vandereycken, Bart; Walach, Hanna
2018
Runge-Kutta time discretization of nonlinear parabolic equations studied via discrete maximal parabolic regularity. Zbl 1410.65347
Kunstmann, Peer C.; Li, Buyang; Lubich, Christian
2018
A low-rank projector-splitting integrator for the Vlasov-Poisson equation. Zbl 1408.35187
Einkemmer, Lukas; Lubich, Christian
2018
Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type. Zbl 1384.65061
Kovács, Balázs; Lubich, Christian
2018
Linearly implicit full discretization of surface evolution. Zbl 1401.65105
Kovács, Balázs; Lubich, Christian
2018
Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations. Zbl 1361.65053
Akrivis, Georgios; Li, Buyang; Lubich, Christian
2017
Numerical analysis of parabolic problems with dynamic boundary conditions. Zbl 1433.65216
Kovács, Balázs; Lubich, Christian
2017
On the nearest singular matrix pencil. Zbl 1371.15015
Guglielmi, Nicola; Lubich, Christian; Mehrmann, Volker
2017
Symmetric multistep methods for charged-particle dynamics. Zbl 1416.78037
Hairer, Ernst; Lubich, Christian
2017
Matrix stabilization using differential equations. Zbl 1379.65037
Guglielmi, Nicola; Lubich, Christian
2017
Convergence of finite elements on an evolving surface driven by diffusion on the surface. Zbl 1377.65131
Kovács, Balázs; Li, Buyang; Lubich, Christian; Power Guerra, Christian A.
2017
Stable and convergent fully discrete interior-exterior coupling of Maxwell’s equations. Zbl 1375.35528
Kovács, Balázs; Lubich, Christian
2017
A-stable time discretizations preserve maximal parabolic regularity. Zbl 1355.65122
Kovács, Balázs; Li, Buyang; Lubich, Christian
2016
Discretized dynamical low-rank approximation in the presence of small singular values. Zbl 1336.65119
Kieri, Emil; Lubich, Christian; Walach, Hanna
2016
Long-term analysis of the Störmer-Verlet method for Hamiltonian systems with a solution-dependent high frequency. Zbl 1408.65100
Hairer, Ernst; Lubich, Christian
2016
Long-term analysis of semilinear wave equations with slowly varying wave speed. Zbl 1368.35164
Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian
2016
Time integration of tensor trains. Zbl 1312.65114
Lubich, Christian; Oseledets, Ivan V.; Vandereycken, Bart
2015
Fully implicit, linearly implicit and implicit-explicit backward difference formulae for quasi-linear parabolic equations. Zbl 1334.65124
Akrivis, Georgios; Lubich, Christian
2015
Stable numerical coupling of exterior and interior problems for the wave equation. Zbl 1314.65122
Banjai, Lehel; Lubich, Christian; Sayas, Francisco-Javier
2015
Low rank differential equations for Hamiltonian matrix nearness problems. Zbl 1312.65070
Guglielmi, Nicola; Kressner, Daniel; Lubich, Christian
2015
Time integration in the multiconfiguration time-dependent Hartree method of molecular quantum dynamics. Zbl 1331.35290
Lubich, Christian
2015
Variational discretization of wave equations on evolving surfaces. Zbl 1307.65136
Lubich, Christian; Mansour, Dhia
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
A projector-splitting integrator for dynamical low-rank approximation. Zbl 1314.65095
Lubich, Christian; Oseledets, Ivan
2014
Energy-diminishing integration of gradient systems. Zbl 1321.65115
Hairer, Ernst; Lubich, Christian
2014
Plane wave stability of the split-step Fourier method for the nonlinear Schrödinger equation. Zbl 1297.65127
Faou, Erwan; Gauckler, Ludwig; Lubich, Christian
2014
Computing extremal points of symplectic pseudospectra and solving symplectic matrix nearness problems. Zbl 1315.65070
Guglielmi, Nicola; Kressner, Daniel; Lubich, Christian
2014
Low-rank dynamics. Zbl 1317.65214
Lubich, Christian
2014
Numerical integrators for motion under a strong constraining force. Zbl 1325.65112
Lubich, Christian; Weiss, Daniel
2014
Dynamical approximation by hierarchical Tucker and tensor-train tensors. Zbl 1391.15087
Lubich, Christian; Rohwedder, Thorsten; Schneider, Reinhold; Vandereycken, Bart
2013
Operator splitting for partial differential equations with Burgers nonlinearity. Zbl 1260.35184
Holden, Helge; Lubich, Christian; Risebro, Nils Henrik
2013
Backward difference time discretization of parabolic differential equations on evolving surfaces. Zbl 1401.65108
Lubich, Christian; Mansour, Dhia; Venkataraman, Chandrasekhar
2013
Low-rank dynamics for computing extremal points of real pseudospectra. Zbl 1272.65032
Guglielmi, Nicola; Lubich, Christian
2013
Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus. Zbl 1274.35357
Faou, Erwan; Gauckler, Ludwig; Lubich, Christian
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
Interior a posteriori error estimates for time discrete approximations of parabolic problems. Zbl 1270.65054
Lubich, Christian; Makridakis, Charalambos
2013
Long-term control of oscillations in differential equations. Zbl 1338.65182
Hairer, Ernst; Lubich, Christian
2013
Runge-Kutta time discretization of parabolic differential equations on evolving surfaces. Zbl 1247.65124
Dziuk, G.; Lubich, Ch.; Mansour, D.
2012
On the energy distribution in Fermi-Pasta-Ulam lattices. Zbl 1283.70011
Hairer, Ernst; Lubich, Christian
2012
Metastable energy strata in weakly nonlinear wave equations. Zbl 1255.35042
Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian; Weiss, Daniel
2012
Erratum/addendum: Differential equations for roaming pseudospectra: paths to extremal points and boundary tracking. Zbl 1257.15007
Guglielmi, Nicola; Lubich, Christian
2012
Runge-Kutta convolution quadrature for operators arising in wave propagation. Zbl 1227.65027
Banjai, Lehel; Lubich, Christian; Melenk, Jens Markus
2011
An error analysis of Runge-Kutta convolution quadrature. Zbl 1228.65245
Banjai, Lehel; Lubich, Christian
2011
Differential equations for roaming pseudospectra: paths to extremal points and boundary tracking. Zbl 1232.15009
Guglielmi, Nicola; Lubich, Christian
2011
Variational-splitting time integration of the multi-configuration time-dependent Hartree-Fock equations in electron dynamics. Zbl 1218.81040
Koch, Othmar; Lubich, Christian
2011
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
Dynamical tensor approximation. Zbl 1214.15017
Koch, Othmar; Lubich, Christian
2010
Splitting integrators for nonlinear Schrödinger equations over long times. Zbl 1189.65301
Gauckler, Ludwig; Lubich, Christian
2010
Nonlinear Schrödinger equations and their spectral semi-discretizations over long times. Zbl 1194.37121
Gauckler, Ludwig; Lubich, Christian
2010
An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics. Zbl 1192.81125
Conte, Dajana; Lubich, Christian
2010
Computing semiclassical quantum dynamics with Hagedorn wavepackets. Zbl 1194.81096
Faou, Erwan; Gradinaru, Vasile; Lubich, Christian
2009
Convergent discretization of heat and wave map flows to spheres using approximate discrete Lagrange multipliers. Zbl 1198.65178
Bartels, Sören; Lubich, Christian; Prohl, Andreas
2009
Oscillation over long times in numerical Hamiltonian systems. Zbl 1180.37121
Hairer, Ernst; Lubich, Christian
2009
On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations. Zbl 1198.65186
Lubich, Christian
2008
From quantum to classical molecular dynamics: Reduced models and numerical analysis. Zbl 1160.81001
Lubich, Christian
2008
Dynamical low-rank approximation. Zbl 1145.65031
Koch, Othmar; Lubich, Christian
2008
Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations. Zbl 1163.65066
Cohen, David; Hairer, Ernst; Lubich, Christian
2008
Adaptive, fast, and oblivious convolution in evolution equations with memory. Zbl 1160.65356
López-Fernández, María; Lubich, Christian; Schädle, Achim
2008
Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions. Zbl 1145.35087
Cohen, David; Hairer, Ernst; Lubich, Christian
2008
Dynamical low-rank approximation: Applications and numerical experiments. Zbl 1162.65335
Nonnenmacher, Achim; Lubich, Christian
2008
Spectral semi-discretisations of weakly non-linear wave equations over long times. Zbl 1156.35007
Hairer, E.; Lubich, C.
2008
Free and constrained symplectic integrators for numerical general relativity. Zbl 1152.83309
Richter, Ronny; Lubich, Christian
2008
Regularity of the multi-configuration time-dependent Hartree approximation in quantum molecular dynamics. Zbl 1135.81380
Koch, Othmar; Lubich, Christian
2007
Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. 2nd ed. Zbl 1094.65125
Hairer, Ernst; Lubich, Christian; Wanner, Gerhard
2006
Convolution quadrature time discretization of fractional diffusion-wave equations. Zbl 1090.65147
Cuesta, Eduardo; Lubich, Christian; Palencia, Cesar
2006
Fast and oblivious convolution quadrature. Zbl 1111.65114
Schädle, Achim; López-Fernández, María; Lubich, Christian
2006
Numerical integrators for highly oscillatory Hamiltonian systems: a review. Zbl 1367.65191
Cohen, David; Jahnke, Tobias; Lorenz, Katina; Lubich, Christian
2006
Numerical energy conservation for multi-frequency oscillatory differential equations. Zbl 1083.65117
Cohen, D.; Hairer, E.; Lubich, Ch.
2005
Fast Runge-Kutta approximation of inhomogeneous parabolic equations. Zbl 1082.65095
López-Fernández, María; Lubich, Christian; Palencia, Cesar; Schädle, Achim
2005
On variational approximations in quantum molecular dynamics. Zbl 1059.81188
Lubich, Christian
2005
Adiabatic integrators for highly oscillatory second-order linear differential equations with time-varying eigendecomposition. Zbl 1077.65077
Lorenz, Katina; Jahnke, Tobias; Lubich, Christian
2005
Lubich, Christian
2004
Symmetric multistep methods over long times. Zbl 1060.65074
Hairer, Ernst; Lubich, Christian
2004
A variational splitting integrator for quantum molecular dynamics. Zbl 1037.81634
Lubich, Christian
2004
Geometric numerical integration illustrated by the Störmer-Verlet method. Zbl 1046.65110
Hairer, Ernst; Lubich, Christian; Wanner, Gerhard
2003
On Magnus integrators for time-dependent Schrödinger equations. Zbl 1049.65064
Hochbruck, Marlis; Lubich, Christian
2003
Modulated Fourier expansions of highly oscillatory differential equations. Zbl 1056.34005
Cohen, David; Hairer, Ernst; Lubich, Christian
2003
Numerical integrators for quantum dynamics close to the adiabatic limit. Zbl 1029.65069
Jahnke, Tobias; Lubich, Christian
2003
Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. Zbl 0994.65135
Hairer, Ernst; Lubich, Christian; Wanner, Gerhard
2002
Fast convolution for nonreflecting boundary conditions. Zbl 1013.65113
Lubich, Christian; Schädle, Achim
2002
Error bounds for exponential operator splittings. Zbl 0972.65061
Jahnke, Tobias; Lubich, Christian
2000
Long-time energy conservation of numerical methods for oscillatory differential equations. Zbl 0988.65118
Hairer, Ernst; Lubich, Christian
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
A Gautschi-type method for oscillatory second-order differential equations. Zbl 0937.65077
Hochbruck, Marlis; Lubich, Christian
1999
Exponential integrators for quantum-classical molecular dynamics. Zbl 0985.81002
Hochbruck, Marlis; Lubich, Christian
1999
Invariant tori of dissipatively perturbed Hamiltonian systems under symplectic discretization. Zbl 1022.37042
Hairer, Ernst; Lubich, Christian
1999
Inertial manifolds of parabolic differential equations under higher-order discretizations. Zbl 0947.65100
van Dorsselaer, Jos L. M.; Lubich, Christian
1999
A bunch of time integrators for quantum/classical molecular dynamics. Zbl 0966.81066
Hochbruk, Marlis; Lubich, Christian
1999
Exponential integrators for large systems of differential equations. Zbl 0912.65058
Hochbruck, Marlis; Lubich, Christian
1998
Periodic orbits of delay differential equations under discretization. Zbl 0904.65066
in’t Hout, Karel J.; Lubich, Christian
1998
Hopf bifurcation of reaction-diffusion and Navier-Stokes equations under discretization. Zbl 0924.65051
Lubich, Christian; Ostermann, Alexander
1998
...and 53 more Documents
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#### Cited by 4,039 Authors

 85 Lubich, Christian 50 Wu, Xinyuan 44 Ostermann, Alexander 41 Hairer, Ernst 35 Xu, Da 33 Wang, Bin 32 Weiner, Rüdiger 30 Chartier, Philippe 28 Li, Buyang 27 Faou, Erwan 26 Murua, Ander 25 Auzinger, Winfried 24 Blanes, Sergio 24 Casas, Fernando 24 Wang, Yushun 21 Sun, Yajuan 20 Schanz, Martin 20 Zhou, Zhi 19 Brugnano, Luigi 19 Celledoni, Elena 19 Deng, Weihua 19 Ford, Neville J. 19 Martín de Diego, David 19 Sandu, Adrian 19 You, Xiong 18 Garrappa, Roberto 18 Iserles, Arieh 18 Koch, Othmar 18 Leok, Melvin 18 Sanz-Serna, Jesús María 18 Sayas, Francisco-Javier 18 Thalhammer, Mechthild 17 Burrage, Kevin 17 McLachlan, Robert I. 17 Vecchio, Antonia 16 Conte, Dajana 16 Einkemmer, Lukas 16 Guglielmi, Nicola 16 Hochbruck, Marlis 16 Hong, Jialin 16 Li, Changpin 16 Owren, Brynjulf 16 Schratz, Katharina 16 Xiao, Aiguo 15 Akrivis, Georgios D. 15 Iavernaro, Felice 15 Montijano, Juan Ignacio 15 Shi, Wei 15 Zeng, Fanhai 14 Arnold, Martin 14 Brunner, Hermann 14 Jin, Bangti 14 Karniadakis, George Em 14 Kulikov, Gennady Yur’evich 14 Li, Jiyong 14 Mustapha, Kassem 14 Simeon, Bernd 14 Tang, Yifa 14 Zhao, Jingjun 14 Zhao, Xiaofei 13 Bao, Weizhu 13 Calvo, Manuel 13 D’Ambrosio, Raffaele 13 Gauckler, Ludwig J. 13 Jimenez, Juan Carlos 13 Palencia, Cesar 13 Rández, Luis 13 Yan, Yubin 12 Banjai, Lehel 12 López-Fernández, María 12 Novati, Paolo 12 Paternoster, Beatrice 12 Quispel, Gilles Reinout Willem 12 Schmitt, Bernhard A. 12 Strehmel, Karl 12 Turner, Ian William 12 Vilmart, Gilles 12 Xu, Yang 12 Zhang, Chuanzeng 11 Butcher, John C. 11 Crouseilles, Nicolas 11 Diele, Fasma 11 Kvaerno, Anne 11 Liu, Fawang 11 Méhats, Florian 11 Miyatake, Yuto 11 Spijker, Marc N. 11 Verwer, Jan G. 10 Aimi, Alessandra 10 Cai, Jiaxiang 10 Campbell, Stephen LaVern 10 Chan, Robert Peng Kong 10 Diligenti, Mauro 10 Falletta, Silvia 10 Gander, Martin Jakob 10 Ju, Lili 10 Karasözen, Bülent 10 Khader, Mohamed M. 10 Kovács, Balázs 10 Kressner, Daniel ...and 3,939 more Authors
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#### Cited in 343 Serials

 279 Journal of Computational and Applied Mathematics 272 Journal of Computational Physics 265 Applied Numerical Mathematics 160 Numerische Mathematik 157 BIT 150 Applied Mathematics and Computation 107 Journal of Scientific Computing 99 Mathematics of Computation 89 SIAM Journal on Scientific Computing 86 Computers & Mathematics with Applications 79 Numerical Algorithms 74 SIAM Journal on Numerical Analysis 71 Computer Methods in Applied Mechanics and Engineering 46 Foundations of Computational Mathematics 43 Computer Physics Communications 39 Engineering Analysis with Boundary Elements 38 Applied Mathematics Letters 35 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 33 International Journal for Numerical Methods in Engineering 33 International Journal of Computer Mathematics 33 Linear Algebra and its Applications 32 Mathematics and Computers in Simulation 31 Advances in Computational Mathematics 28 Fractional Calculus & Applied Analysis 27 Journal of Mathematical Analysis and Applications 26 Computing 25 SIAM Journal on Matrix Analysis and Applications 25 Communications in Nonlinear Science and Numerical Simulation 23 Applied Mathematical Modelling 22 Discrete and Continuous Dynamical Systems 20 Journal of Integral Equations and Applications 19 Calcolo 19 Physica D 19 Computational Mechanics 18 Discrete and Continuous Dynamical Systems. Series B 17 Multibody System Dynamics 16 Numerical Methods for Partial Differential Equations 16 Nonlinear Dynamics 15 Physics Letters. A 15 Numerical Linear Algebra with Applications 15 Computational Methods in Applied Mathematics 14 Journal of Mathematical Physics 14 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 14 Multiscale Modeling & Simulation 14 Advances in Difference Equations 13 Celestial Mechanics and Dynamical Astronomy 13 Computational and Applied Mathematics 12 Mathematical and Computer Modelling 11 Chaos, Solitons and Fractals 11 Journal of Mathematical Chemistry 10 Numerical Functional Analysis and Optimization 10 Abstract and Applied Analysis 10 Journal of Computational Dynamics 9 Wave Motion 9 Journal of Nonlinear Science 9 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 8 Computers and Fluids 8 Communications in Mathematical Physics 8 Nonlinearity 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Systems & Control Letters 8 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 8 ETNA. Electronic Transactions on Numerical Analysis 8 Journal of Difference Equations and Applications 8 Journal of Applied Mathematics and Computing 8 Acta Numerica 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Automatica 7 Journal of Differential Equations 7 Mathematical Problems in Engineering 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 International Journal of Control 6 Mathematical Methods in the Applied Sciences 6 Applied Mathematics and Mechanics. (English Edition) 6 Journal of Complexity 6 Japan Journal of Industrial and Applied Mathematics 6 SIAM Journal on Mathematical Analysis 5 Applicable Analysis 5 Archive for Rational Mechanics and Analysis 5 Journal of Engineering Mathematics 5 Journal of Fluid Mechanics 5 Acta Mathematicae Applicatae Sinica. English Series 5 Optimization Methods & Software 5 Differential Equations 5 Journal of Applied Mathematics 5 Mediterranean Journal of Mathematics 5 Discrete and Continuous Dynamical Systems. Series S 5 Journal of Geometric Mechanics 5 Science China. Mathematics 5 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 5 Journal of Applied Analysis and Computation 5 Axioms 5 Mathematics 5 International Journal of Applied and Computational Mathematics 5 Communications on Applied Mathematics and Computation 4 Acta Mechanica 4 Journal of the Franklin Institute 4 Journal of Statistical Physics 4 Letters in Mathematical Physics 4 Journal of Functional Analysis ...and 243 more Serials
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#### Cited in 56 Fields

 2,824 Numerical analysis (65-XX) 1,032 Partial differential equations (35-XX) 782 Ordinary differential equations (34-XX) 425 Dynamical systems and ergodic theory (37-XX) 285 Integral equations (45-XX) 279 Mechanics of particles and systems (70-XX) 226 Fluid mechanics (76-XX) 217 Mechanics of deformable solids (74-XX) 140 Real functions (26-XX) 131 Linear and multilinear algebra; matrix theory (15-XX) 124 Probability theory and stochastic processes (60-XX) 121 Statistical mechanics, structure of matter (82-XX) 116 Quantum theory (81-XX) 97 Systems theory; control (93-XX) 88 Optics, electromagnetic theory (78-XX) 85 Biology and other natural sciences (92-XX) 79 Calculus of variations and optimal control; optimization (49-XX) 69 Operator theory (47-XX) 49 Difference and functional equations (39-XX) 40 Differential geometry (53-XX) 38 Approximations and expansions (41-XX) 35 Computer science (68-XX) 29 Information and communication theory, circuits (94-XX) 27 Integral transforms, operational calculus (44-XX) 27 Geophysics (86-XX) 27 Operations research, mathematical programming (90-XX) 26 Classical thermodynamics, heat transfer (80-XX) 26 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 23 Statistics (62-XX) 21 Global analysis, analysis on manifolds (58-XX) 19 Special functions (33-XX) 17 Combinatorics (05-XX) 14 Nonassociative rings and algebras (17-XX) 14 Topological groups, Lie groups (22-XX) 11 Associative rings and algebras (16-XX) 11 Functional analysis (46-XX) 10 History and biography (01-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 9 Relativity and gravitational theory (83-XX) 7 General and overarching topics; collections (00-XX) 6 Astronomy and astrophysics (85-XX) 4 Algebraic geometry (14-XX) 4 Functions of a complex variable (30-XX) 4 Potential theory (31-XX) 3 Manifolds and cell complexes (57-XX) 2 Mathematical logic and foundations (03-XX) 2 Number theory (11-XX) 2 Commutative algebra (13-XX) 2 Category theory; homological algebra (18-XX) 2 Geometry (51-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX)

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