Edit Profile (opens in new tab) Lubich, Christian Co-Author Distance Author ID: lubich.christian Published as: Lubich, Christian; Lubich, Ch.; Lubich, C. more...less Homepage: https://na.uni-tuebingen.de/~lubich/ External Links: MGP · ORCID · Wikidata · dblp · GND · IdRef Documents Indexed: 188 Publications since 1982, including 5 Books and 10 Additional arXiv Preprints 4 Contributions as Editor Software Indexed: 2 Packages Co-Authors: 77 Co-Authors with 162 Joint Publications 2,093 Co-Co-Authors all top 5 Co-Authors 30 single-authored 48 Hairer, Ernst 14 Guglielmi, Nicola 13 Kovacs, Balazs A. 11 Hochbruck, Marlis 9 Gauckler, Ludwig J. 8 Ceruti, Gianluca 7 Li, Buyang 7 Ostermann, Alexander 6 Cohen, David 6 Nick, Jörg 5 Banjai, Lehel 5 Faou, Erwan 5 Jahnke, Tobias 4 Edelmann, Dominik 4 Koch, Othmar 4 Kusch, Jonas 4 Roche, Michel 4 Schädle, Achim 4 Shi, Yanyan 4 Wanner, Gerhard 3 Akrivis, Georgios D. 3 Andreotti, Eleonora 3 Eggermont, Paul P. B. 3 Einkemmer, Lukas 3 López-Fernández, María 3 Mansour, Dhia 3 Vandereycken, Bart 3 Walach, Hanna 2 Engstler, Christian 2 Feischl, Michael 2 Iserles, Arieh 2 Kressner, Daniel 2 Lasser, Caroline 2 Lorenz, Katina 2 Oseledets, Ivan Valer’evich 2 Palencia, Cesar 2 Schlichte, M. 2 Schneider, Reinhold 2 Sulz, Dominik 2 Weiss, Daniel Alexander 1 Bartels, Sören 1 Baumstark, Julian 1 Brügmann, Bernd 1 Burkhard, Selina 1 Console, Paola 1 Conte, Dajana 1 Cuesta, Eduardo 1 Dziuk, Gerhard 1 Fazzi, Antonio 1 Gradinaru, Vasile 1 Holden, Helge 1 in ’t Hout, Karel J. 1 Kieri, Emil 1 Kunstmann, Peer Christian 1 Makridakis, Charalambos G. 1 McLachlan, Robert I. 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 Sanz-Serna, Jesús María 1 Sayas, Francisco-Javier 1 Sicilia, Stefano 1 Sloan, Ian Hugh 1 Stoffer, Daniel 1 Thomée, Vidar 1 van Dorsselaer, Jos L. M. 1 Venkataraman, Chandrasekhar 1 Walther, Benny 1 Wang, Bin all top 5 Serials 35 Numerische Mathematik 22 BIT 17 SIAM Journal on Numerical Analysis 15 Mathematics of Computation 12 IMA Journal of Numerical Analysis 9 SIAM Journal on Scientific Computing 8 SIAM Journal on Matrix Analysis and Applications 6 Applied Numerical Mathematics 5 Foundations of Computational Mathematics 4 Oberwolfach Reports 3 Communications in Partial Differential Equations 3 Springer Series in Computational Mathematics 2 Archive for Rational Mechanics and Analysis 2 Computing 2 IMPACT of Computing in Science and Engineering 2 Acta Numerica 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 Computing and Visualization in Science 1 Interfaces and Free Boundaries 1 AMRX. Applied Mathematics Research eXpress 1 Multiscale Modeling & Simulation 1 Lecture Notes in Mathematics 1 Forum of Mathematics, Sigma 1 Zurich Lectures in Advanced Mathematics 1 SMAI Journal of Computational Mathematics all top 5 Fields 168 Numerical analysis (65-XX) 59 Partial differential equations (35-XX) 49 Ordinary differential equations (34-XX) 27 Dynamical systems and ergodic theory (37-XX) 24 Linear and multilinear algebra; matrix theory (15-XX) 23 Integral equations (45-XX) 15 Mechanics of particles and systems (70-XX) 13 Quantum theory (81-XX) 8 Optics, electromagnetic theory (78-XX) 6 Integral transforms, operational calculus (44-XX) 4 General and overarching topics; collections (00-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Statistical mechanics, structure of matter (82-XX) 4 Systems theory; control (93-XX) 3 Fluid mechanics (76-XX) 2 Combinatorics (05-XX) 2 Real functions (26-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Computer science (68-XX) 2 Operations research, mathematical programming (90-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 Relativity and gravitational theory (83-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 176 Publications have been cited 9,591 times in 5,613 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 1,513 2006 Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. Zbl 0994.65135 Hairer, Ernst; Lubich, Christian; Wanner, Gerhard 618 2002 Discretized fractional calculus. Zbl 0624.65015 Lubich, Ch. 499 1986 Convolution quadrature and discretized operational calculus. I. Zbl 0637.65016 Lubich, C. 400 1988 On Krylov subspace approximations to the matrix exponential operator. Zbl 0888.65032 Hochbruck, Marlis; Lubich, Christian 297 1997 Exponential integrators for large systems of differential equations. Zbl 0912.65058 Hochbruck, Marlis; Lubich, Christian 242 1998 The numerical solution of differential-algebraic systems by Runge-Kutta methods. Zbl 0683.65050 Hairer, Ernst; Lubich, Christian; Roche, Michel 224 1989 Convolution quadrature and discretized operational calculus. II. Zbl 0643.65094 Lubich, C. 203 1988 Convolution quadrature time discretization of fractional diffusion-wave equations. Zbl 1090.65147 Cuesta, Eduardo; Lubich, Christian; Palencia, Cesar 198 2006 On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations. Zbl 1198.65186 Lubich, Christian 191 2008 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. 165 1996 From quantum to classical molecular dynamics: Reduced models and numerical analysis. Zbl 1160.81001 Lubich, Christian 155 2008 Geometric numerical integration illustrated by the Störmer-Verlet method. Zbl 1046.65110 Hairer, Ernst; Lubich, Christian; Wanner, Gerhard 148 2003 Dynamical low-rank approximation. Zbl 1145.65031 Koch, Othmar; Lubich, Christian 148 2007 A Gautschi-type method for oscillatory second-order differential equations. Zbl 0937.65077 Hochbruck, Marlis; Lubich, Christian 135 1999 Fast convolution for nonreflecting boundary conditions. Zbl 1013.65113 Lubich, Christian; Schädle, Achim 122 2002 On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations. Zbl 0795.65063 Lubich, Ch. 120 1994 Long-time energy conservation of numerical methods for oscillatory differential equations. Zbl 0988.65118 Hairer, Ernst; Lubich, Christian 120 2000 Fractional linear multistep methods for Abel-Volterra integral equations of the second kind. Zbl 0584.65090 Lubich, Ch. 115 1985 Error bounds for exponential operator splittings. Zbl 0972.65061 Jahnke, Tobias; Lubich, Christian 115 2000 Convolution quadrature revisited. Zbl 1083.65123 Lubich, Christian 105 2004 Fast and oblivious convolution quadrature. Zbl 1111.65114 Schädle, Achim; López-Fernández, María; Lubich, Christian 99 2006 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 99 2010 A projector-splitting integrator for dynamical low-rank approximation. Zbl 1314.65095 Lubich, Christian; Oseledets, Ivan 88 2014 Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations. Zbl 0657.65093 Hairer, E.; Lubich, Ch.; Roche, M. 83 1988 Fast numerical solution of nonlinear Volterra convolution equations. Zbl 0581.65095 Hairer, E.; Lubich, Ch.; Schlichte, M. 79 1985 Runge-Kutta theory for Volterra and Abel integral equations of the second kind. Zbl 0538.65091 Lubich, Ch. 79 1983 Runge-Kutta methods for parabolic equations and convolution quadrature. Zbl 0795.65062 Lubich, Ch.; Ostermann, A. 78 1993 On the stability of linear multistep methods for Volterra convolution equations. Zbl 0543.65095 Lubich, Ch. 70 1983 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 Dynamical tensor approximation. Zbl 1214.15017 Koch, Othmar; Lubich, Christian 68 2010 Multi-grid dynamic iteration for parabolic equations. Zbl 0623.65125 Lubich, Ch.; Ostermann, A. 67 1987 Runge-Kutta approximation of quasi-linear parabolic equations. Zbl 0832.65104 Lubich, Christian; Ostermann, Alexander 58 1995 The life-span of backward error analysis for numerical integrators. Zbl 0874.65061 Hairer, E.; Lubich, Ch. 58 1997 Linearly implicit time discretization of nonlinear parabolic equations. Zbl 0834.65092 Lubich, Ch.; Ostermann, A. 57 1995 Discretized dynamical low-rank approximation in the presence of small singular values. Zbl 1336.65119 Kieri, Emil; Lubich, Christian; Walach, Hanna 56 2016 Time integration of tensor trains. Zbl 1312.65114 Lubich, Christian; Oseledets, Ivan V.; Vandereycken, Bart 53 2015 Dynamical approximation by hierarchical Tucker and tensor-train tensors. Zbl 1391.15087 Lubich, Christian; Rohwedder, Thorsten; Schneider, Reinhold; Vandereycken, Bart 53 2013 A stability analysis of convolution quadratures for Abel-Volterra integral equations. Zbl 0587.65090 Lubich, Ch. 52 1986 Adaptive, fast, and oblivious convolution in evolution equations with memory. Zbl 1160.65356 López-Fernández, María; Lubich, Christian; Schädle, Achim 49 2008 A low-rank projector-splitting integrator for the Vlasov-Poisson equation. Zbl 1408.35187 Einkemmer, Lukas; Lubich, Christian 49 2018 Backward difference time discretization of parabolic differential equations on evolving surfaces. Zbl 1401.65108 Lubich, Christian; Mansour, Dhia; Venkataraman, Chandrasekhar 48 2013 Runge-Kutta convolution quadrature for operators arising in wave propagation. Zbl 1227.65027 Banjai, Lehel; Lubich, Christian; Melenk, Jens Markus 48 2011 On resolvent conditions and stability estimates. Zbl 0731.65043 Lubich, Christian; Nevanlinna, Olavi 46 1991 Operator splitting for partial differential equations with Burgers nonlinearity. Zbl 1260.35184 Holden, Helge; Lubich, Christian; Risebro, Nils Henrik 45 2013 A convergent evolving finite element algorithm for mean curvature flow of closed surfaces. Zbl 1427.65250 Kovács, Balázs; Li, Buyang; Lubich, Christian 43 2019 An unconventional robust integrator for dynamical low-rank approximation. Zbl 1481.65068 Ceruti, Gianluca; Lubich, Christian 43 2022 Stable numerical coupling of exterior and interior problems for the wave equation. Zbl 1314.65122 Banjai, Lehel; Lubich, Christian; Sayas, Francisco-Javier 42 2015 Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations. Zbl 1361.65053 Akrivis, Georgios; Li, Buyang; Lubich, Christian 41 2017 A-stable time discretizations preserve maximal parabolic regularity. Zbl 1355.65122 Kovács, Balázs; Li, Buyang; Lubich, Christian 40 2016 Splitting integrators for nonlinear Schrödinger equations over long times. Zbl 1189.65301 Gauckler, Ludwig; Lubich, Christian 40 2010 Energy-diminishing integration of gradient systems. Zbl 1321.65115 Hairer, Ernst; Lubich, Christian 39 2014 On the stability of semi-implicit methods for ordinary differential equations. Zbl 0489.65046 Hairer, E.; Bader, G.; Lubich, Ch. 39 1982 Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions. Zbl 1145.35087 Cohen, David; Hairer, Ernst; Lubich, Christian 39 2008 Time discretization of parabolic boundary integral equations. Zbl 0795.65061 Lubich, Ch.; Schneider, R. 38 1992 Fully implicit, linearly implicit and implicit-explicit backward difference formulae for quasi-linear parabolic equations. Zbl 1334.65124 Akrivis, Georgios; Lubich, Christian 38 2015 Error of Rosenbrock methods for stiff problems studied via differential algebraic equations. Zbl 0674.65039 Hairer, E.; Lubich, Ch.; Roche, M. 36 1989 Numerical energy conservation for multi-frequency oscillatory differential equations. Zbl 1083.65117 Cohen, D.; Hairer, E.; Lubich, Ch. 34 2005 Fast numerical solution of weakly singular Volterra integral equations. Zbl 0654.65091 Hairer, E.; Lubich, Ch.; Schlichte, M. 34 1988 Computing semiclassical quantum dynamics with Hagedorn wavepackets. Zbl 1194.81096 Faou, Erwan; Gradinaru, Vasile; Lubich, Christian 34 2009 Modulated Fourier expansions of highly oscillatory differential equations. Zbl 1056.34005 Cohen, David; Hairer, Ernst; Lubich, Christian 33 2003 Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus. Zbl 1274.35357 Faou, Erwan; Gauckler, Ludwig; Lubich, Christian 33 2013 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 Exponential integrators for quantum-classical molecular dynamics. Zbl 0985.81002 Hochbruck, Marlis; Lubich, Christian 33 1999 Dynamical low-rank approximation: Applications and numerical experiments. Zbl 1162.65335 Nonnenmacher, Achim; Lubich, Christian 32 2008 On the convergence of multistep methods for nonlinear stiff differential equations. Zbl 0729.65055 Lubich, C. 31 1991 A rank-adaptive robust integrator for dynamical low-rank approximation. Zbl 1507.65116 Ceruti, Gianluca; Kusch, Jonas; Lubich, Christian 31 2022 A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field. Zbl 1434.65312 Hairer, Ernst; Lubich, Christian; Wang, Bin 30 2020 Numerical integrators for highly oscillatory Hamiltonian systems: a review. Zbl 1367.65191 Cohen, David; Jahnke, Tobias; Lorenz, Katina; Lubich, Christian 30 2006 On Magnus integrators for time-dependent Schrödinger equations. Zbl 1049.65064 Hochbruck, Marlis; Lubich, Christian 30 2003 Computing quantum dynamics in the semiclassical regime. Zbl 07674564 Lasser, Caroline; Lubich, Christian 30 2020 Nonlinear Schrödinger equations and their spectral semi-discretizations over long times. Zbl 1194.37121 Gauckler, Ludwig; Lubich, Christian 29 2010 Runge-Kutta theory for Volterra integrodifferential equations. Zbl 0491.65064 Lubich, Ch. 28 1982 An error analysis of Runge-Kutta convolution quadrature. Zbl 1228.65245 Banjai, Lehel; Lubich, Christian 28 2011 Energy behaviour of the Boris method for charged-particle dynamics. Zbl 1404.65309 Hairer, Ernst; Lubich, Christian 28 2018 Multirate extrapolation methods for differential equations with different time scales. Zbl 0891.65083 Engstler, Ch.; Lubich, Ch. 27 1997 Symmetric multistep methods for charged-particle dynamics. Zbl 1416.78037 Hairer, Ernst; Lubich, Christian 27 2017 A quasi-conservative Dynamical Low-rank algorithm for the Vlasov equation. Zbl 1428.82058 Einkemmer, Lukas; Lubich, Christian 27 2019 Symmetric multistep methods over long times. Zbl 1060.65074 Hairer, Ernst; Lubich, Christian 26 2004 Asymptotic expansions of the global error of fixed-stepsize methods. Zbl 0571.65066 Hairer, E.; Lubich, C. 26 1984 Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field. Zbl 1432.78013 Hairer, Ernst; Lubich, Christian 26 2020 Time integration of rank-constrained Tucker tensors. Zbl 1407.37113 Lubich, Christian; Vandereycken, Bart; Walach, Hanna 26 2018 Extrapolation integrators for constrained multibody systems. Zbl 0742.70011 Lubich, Ch. 25 1991 Integration of stiff mechanical systems by Runge-Kutta methods. Zbl 0784.70002 Lubich, Ch. 23 1993 Spectral semi-discretisations of weakly non-linear wave equations over long times. Zbl 1156.35007 Hairer, E.; Lubich, C. 23 2008 Low-rank dynamics for computing extremal points of real pseudospectra. Zbl 1272.65032 Guglielmi, Nicola; Lubich, Christian 23 2013 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 22 1996 Numerical analysis of parabolic problems with dynamic boundary conditions. Zbl 1433.65216 Kovács, Balázs; Lubich, Christian 22 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. 21 2017 Fractional linear multistep methods for Abel Volterra integral equations of the first kind. Zbl 0624.65137 Lubich, Ch. 21 1987 Runge-Kutta time discretization of parabolic differential equations on evolving surfaces. Zbl 1247.65124 Dziuk, G.; Lubich, Ch.; Mansour, D. 21 2012 Time integration in the multiconfiguration time-dependent Hartree method of molecular quantum dynamics. Zbl 1331.35290 Lubich, Christian 20 2015 On variational approximations in quantum molecular dynamics. Zbl 1059.81188 Lubich, Christian 20 2005 On the nearest singular matrix pencil. Zbl 1371.15015 Guglielmi, Nicola; Lubich, Christian; Mehrmann, Volker 19 2017 On convolution quadrature and Hille-Phillips operational calculus. Zbl 0747.65013 Lubich, C. 19 1992 A Convergent evolving finite element algorithm for Willmore flow of closed surfaces. Zbl 1496.65165 Kovács, Balázs; Li, Buyang; Lubich, Christian 19 2021 Differential equations for roaming pseudospectra: paths to extremal points and boundary tracking. Zbl 1232.15009 Guglielmi, Nicola; Lubich, Christian 19 2011 Low rank differential equations for Hamiltonian matrix nearness problems. Zbl 1312.65070 Guglielmi, Nicola; Kressner, Daniel; Lubich, Christian 18 2015 A Poisson integrator for Gaussian wavepacket dynamics. Zbl 1511.65108 Faou, Erwan; Lubich, Christian 18 2006 Fast Runge-Kutta approximation of inhomogeneous parabolic equations. Zbl 1082.65095 López-Fernández, María; Lubich, Christian; Palencia, Cesar; Schädle, Achim 18 2005 A parallel rank-adaptive integrator for dynamical low-rank approximation. Zbl 07843961 Ceruti, Gianluca; Kusch, Jonas; Lubich, Christian 1 2024 Rank-adaptive time integration of tree tensor networks. Zbl 1511.65064 Ceruti, Gianluca; Lubich, Christian; Sulz, Dominik 9 2023 On a large-stepsize integrator for charged-particle dynamics. Zbl 1507.65289 Lubich, Christian; Shi, Yanyan 1 2023 Rank-1 matrix differential equations for structured eigenvalue optimization. Zbl 1520.65044 Guglielmi, Nicola; Lubich, Christian; Sicilia, Stefano 1 2023 An unconventional robust integrator for dynamical low-rank approximation. Zbl 1481.65068 Ceruti, Gianluca; Lubich, Christian 43 2022 A rank-adaptive robust integrator for dynamical low-rank approximation. Zbl 1507.65116 Ceruti, Gianluca; Kusch, Jonas; Lubich, Christian 31 2022 Large-stepsize integrators for charged-particle dynamics over multiple time scales. Zbl 1510.65314 Hairer, Ernst; Lubich, Christian; Shi, Yanyan 8 2022 Time-dependent acoustic scattering from generalized impedance boundary conditions via boundary elements and convolution quadrature. Zbl 1529.65137 Banjai, Lehel; Lubich, Christian; Nick, Jörg 5 2022 Time-dependent electromagnetic scattering from thin layers. Zbl 1491.35408 Nick, Jörg; Kovács, Balázs; Lubich, Christian 3 2022 A Convergent evolving finite element algorithm for Willmore flow of closed surfaces. Zbl 1496.65165 Kovács, Balázs; Li, Buyang; Lubich, Christian 19 2021 Higher-order linearly implicit full discretization of the Landau-Lifshitz-Gilbert equation. Zbl 1466.65114 Akrivis, Georgios; Feischl, Michael; Kovács, Balázs; Lubich, Christian 14 2021 Time integration of tree tensor networks. Zbl 1461.65203 Ceruti, Gianluca; Lubich, Christian; Walach, Hanna 11 2021 Finding the nearest passive or nonpassive system via Hamiltonian eigenvalue optimization. Zbl 1483.65097 Fazzi, Antonio; Guglielmi, Nicola; Lubich, Christian 3 2021 Measuring the stability of spectral clustering. Zbl 1460.65065 Andreotti, Eleonora; Edelmann, Dominik; Guglielmi, Nicola; Lubich, Christian 2 2021 Correction to: “Stable and convergent fully discrete interior-exterior coupling of Maxwell’s equations”. Zbl 1467.35308 Nick, Jörg; Kovács, Balázs; Lubich, Christian 2 2021 A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field. Zbl 1434.65312 Hairer, Ernst; Lubich, Christian; Wang, Bin 30 2020 Computing quantum dynamics in the semiclassical regime. Zbl 07674564 Lasser, Caroline; Lubich, Christian 30 2020 Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field. Zbl 1432.78013 Hairer, Ernst; Lubich, Christian 26 2020 A convergent algorithm for forced mean curvature flow driven by diffusion on the surface. Zbl 1458.35016 Kovács, Balázs; Li, Buyang; Lubich, Christian 11 2020 Time integration of symmetric and anti-symmetric low-rank matrices and Tucker tensors. Zbl 1446.65037 Ceruti, Gianluca; Lubich, Christian 10 2020 A convergent evolving finite element algorithm for mean curvature flow of closed surfaces. Zbl 1427.65250 Kovács, Balázs; Li, Buyang; Lubich, Christian 43 2019 A quasi-conservative Dynamical Low-rank algorithm for the Vlasov equation. Zbl 1428.82058 Einkemmer, Lukas; Lubich, Christian 27 2019 Runge-Kutta convolution coercivity and its use for time-dependent boundary integral equations. Zbl 1464.65074 Banjai, Lehel; Lubich, Christian 7 2019 Constrained graph partitioning via matrix differential equations. Zbl 1407.05187 Andreotti, Eleonora; Edelmann, Dominik; Guglielmi, Nicola; Lubich, Christian 2 2019 A low-rank projector-splitting integrator for the Vlasov-Poisson equation. Zbl 1408.35187 Einkemmer, Lukas; Lubich, Christian 49 2018 Energy behaviour of the Boris method for charged-particle dynamics. Zbl 1404.65309 Hairer, Ernst; Lubich, Christian 28 2018 Time integration of rank-constrained Tucker tensors. Zbl 1407.37113 Lubich, Christian; Vandereycken, Bart; Walach, Hanna 26 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 16 2018 Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type. Zbl 1384.65061 Kovács, Balázs; Lubich, Christian 9 2018 Linearly implicit full discretization of surface evolution. Zbl 1401.65105 Kovács, Balázs; Lubich, Christian 8 2018 Dynamics, numerical analysis, and some geometry. Zbl 1451.62056 Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian 8 2018 Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations. Zbl 1361.65053 Akrivis, Georgios; Li, Buyang; Lubich, Christian 41 2017 Symmetric multistep methods for charged-particle dynamics. Zbl 1416.78037 Hairer, Ernst; Lubich, Christian 27 2017 Numerical analysis of parabolic problems with dynamic boundary conditions. Zbl 1433.65216 Kovács, Balázs; Lubich, Christian 22 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. 21 2017 On the nearest singular matrix pencil. Zbl 1371.15015 Guglielmi, Nicola; Lubich, Christian; Mehrmann, Volker 19 2017 Stable and convergent fully discrete interior-exterior coupling of Maxwell’s equations. Zbl 1375.35528 Kovács, Balázs; Lubich, Christian 11 2017 Matrix stabilization using differential equations. Zbl 1379.65037 Guglielmi, Nicola; Lubich, Christian 11 2017 Discretized dynamical low-rank approximation in the presence of small singular values. Zbl 1336.65119 Kieri, Emil; Lubich, Christian; Walach, Hanna 56 2016 A-stable time discretizations preserve maximal parabolic regularity. Zbl 1355.65122 Kovács, Balázs; Li, Buyang; Lubich, Christian 40 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 16 2016 Long-term analysis of semilinear wave equations with slowly varying wave speed. Zbl 1368.35164 Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian 5 2016 Time integration of tensor trains. Zbl 1312.65114 Lubich, Christian; Oseledets, Ivan V.; Vandereycken, Bart 53 2015 Stable numerical coupling of exterior and interior problems for the wave equation. Zbl 1314.65122 Banjai, Lehel; Lubich, Christian; Sayas, Francisco-Javier 42 2015 Fully implicit, linearly implicit and implicit-explicit backward difference formulae for quasi-linear parabolic equations. Zbl 1334.65124 Akrivis, Georgios; Lubich, Christian 38 2015 Time integration in the multiconfiguration time-dependent Hartree method of molecular quantum dynamics. Zbl 1331.35290 Lubich, Christian 20 2015 Low rank differential equations for Hamiltonian matrix nearness problems. Zbl 1312.65070 Guglielmi, Nicola; Kressner, Daniel; Lubich, Christian 18 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 Variational discretization of wave equations on evolving surfaces. Zbl 1307.65136 Lubich, Christian; Mansour, Dhia 11 2015 A projector-splitting integrator for dynamical low-rank approximation. Zbl 1314.65095 Lubich, Christian; Oseledets, Ivan 88 2014 Energy-diminishing integration of gradient systems. Zbl 1321.65115 Hairer, Ernst; Lubich, Christian 39 2014 Plane wave stability of the split-step Fourier method for the nonlinear Schrödinger equation. Zbl 1297.65127 Faou, Erwan; Gauckler, Ludwig; Lubich, Christian 14 2014 Computing extremal points of symplectic pseudospectra and solving symplectic matrix nearness problems. Zbl 1315.65070 Guglielmi, Nicola; Kressner, Daniel; Lubich, Christian 2 2014 Numerical integrators for motion under a strong constraining force. Zbl 1325.65112 Lubich, Christian; Weiss, Daniel 1 2014 Low-rank dynamics. Zbl 1317.65214 Lubich, Christian 1 2014 Dynamical approximation by hierarchical Tucker and tensor-train tensors. Zbl 1391.15087 Lubich, Christian; Rohwedder, Thorsten; Schneider, Reinhold; Vandereycken, Bart 53 2013 Backward difference time discretization of parabolic differential equations on evolving surfaces. Zbl 1401.65108 Lubich, Christian; Mansour, Dhia; Venkataraman, Chandrasekhar 48 2013 Operator splitting for partial differential equations with Burgers nonlinearity. Zbl 1260.35184 Holden, Helge; Lubich, Christian; Risebro, Nils Henrik 45 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 33 2013 Low-rank dynamics for computing extremal points of real pseudospectra. Zbl 1272.65032 Guglielmi, Nicola; Lubich, Christian 23 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 6 2013 Long-term control of oscillations in differential equations. Zbl 1338.65182 Hairer, Ernst; Lubich, Christian 3 2013 Interior a posteriori error estimates for time discrete approximations of parabolic problems. Zbl 1270.65054 Lubich, Christian; Makridakis, Charalambos 3 2013 Runge-Kutta time discretization of parabolic differential equations on evolving surfaces. Zbl 1247.65124 Dziuk, G.; Lubich, Ch.; Mansour, D. 21 2012 On the energy distribution in Fermi-Pasta-Ulam lattices. Zbl 1283.70011 Hairer, Ernst; Lubich, Christian 10 2012 Metastable energy strata in weakly nonlinear wave equations. Zbl 1255.35042 Gauckler, Ludwig; Hairer, Ernst; Lubich, Christian; Weiss, Daniel 6 2012 Erratum/addendum: Differential equations for roaming pseudospectra: paths to extremal points and boundary tracking. Zbl 1257.15007 Guglielmi, Nicola; Lubich, Christian 4 2012 Runge-Kutta convolution quadrature for operators arising in wave propagation. Zbl 1227.65027 Banjai, Lehel; Lubich, Christian; Melenk, Jens Markus 48 2011 An error analysis of Runge-Kutta convolution quadrature. Zbl 1228.65245 Banjai, Lehel; Lubich, Christian 28 2011 Differential equations for roaming pseudospectra: paths to extremal points and boundary tracking. Zbl 1232.15009 Guglielmi, Nicola; Lubich, Christian 19 2011 Variational-splitting time integration of the multi-configuration time-dependent Hartree-Fock equations in electron dynamics. Zbl 1218.81040 Koch, Othmar; Lubich, Christian 8 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 99 2010 Dynamical tensor approximation. Zbl 1214.15017 Koch, Othmar; Lubich, Christian 68 2010 Splitting integrators for nonlinear Schrödinger equations over long times. Zbl 1189.65301 Gauckler, Ludwig; Lubich, Christian 40 2010 Nonlinear Schrödinger equations and their spectral semi-discretizations over long times. Zbl 1194.37121 Gauckler, Ludwig; Lubich, Christian 29 2010 An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics. Zbl 1192.81125 Conte, Dajana; Lubich, Christian 14 2010 Computing semiclassical quantum dynamics with Hagedorn wavepackets. Zbl 1194.81096 Faou, Erwan; Gradinaru, Vasile; Lubich, Christian 34 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 13 2009 Oscillation over long times in numerical Hamiltonian systems. Zbl 1180.37121 Hairer, Ernst; Lubich, Christian 10 2009 On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations. Zbl 1198.65186 Lubich, Christian 191 2008 From quantum to classical molecular dynamics: Reduced models and numerical analysis. Zbl 1160.81001 Lubich, Christian 155 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 Adaptive, fast, and oblivious convolution in evolution equations with memory. Zbl 1160.65356 López-Fernández, María; Lubich, Christian; Schädle, Achim 49 2008 Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions. Zbl 1145.35087 Cohen, David; Hairer, Ernst; Lubich, Christian 39 2008 Dynamical low-rank approximation: Applications and numerical experiments. Zbl 1162.65335 Nonnenmacher, Achim; Lubich, Christian 32 2008 Spectral semi-discretisations of weakly non-linear wave equations over long times. Zbl 1156.35007 Hairer, E.; Lubich, C. 23 2008 Free and constrained symplectic integrators for numerical general relativity. Zbl 1152.83309 Richter, Ronny; Lubich, Christian 3 2008 Dynamical low-rank approximation. Zbl 1145.65031 Koch, Othmar; Lubich, Christian 148 2007 Regularity of the multi-configuration time-dependent Hartree approximation in quantum molecular dynamics. Zbl 1135.81380 Koch, Othmar; Lubich, Christian 14 2007 Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. 2nd ed. Zbl 1094.65125 Hairer, Ernst; Lubich, Christian; Wanner, Gerhard 1,513 2006 Convolution quadrature time discretization of fractional diffusion-wave equations. Zbl 1090.65147 Cuesta, Eduardo; Lubich, Christian; Palencia, Cesar 198 2006 Fast and oblivious convolution quadrature. Zbl 1111.65114 Schädle, Achim; López-Fernández, María; Lubich, Christian 99 2006 Numerical integrators for highly oscillatory Hamiltonian systems: a review. Zbl 1367.65191 Cohen, David; Jahnke, Tobias; Lorenz, Katina; Lubich, Christian 30 2006 A Poisson integrator for Gaussian wavepacket dynamics. Zbl 1511.65108 Faou, Erwan; Lubich, Christian 18 2006 Report 14/2006: Geometric Numerical Integration (March 19th – March 25th, 2006). Zbl 1109.65301 15 2006 Numerical energy conservation for multi-frequency oscillatory differential equations. Zbl 1083.65117 Cohen, D.; Hairer, E.; Lubich, Ch. 34 2005 On variational approximations in quantum molecular dynamics. Zbl 1059.81188 Lubich, Christian 20 2005 Fast Runge-Kutta approximation of inhomogeneous parabolic equations. Zbl 1082.65095 López-Fernández, María; Lubich, Christian; Palencia, Cesar; Schädle, Achim 18 2005 ...and 76 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 5,919 Authors 102 Lubich, Christian 64 Wang, Bin 62 Wu, Xinyuan 60 Wang, Yushun 55 Ostermann, Alexander 53 Xu, Da 49 Li, Buyang 46 Hairer, Ernst 41 Blanes, Sergio 39 Casas, Fernando 34 Chartier, Philippe 34 Weiner, Rüdiger 33 Cai, Wenjun 33 Einkemmer, Lukas 33 Murua, Ander 31 Bao, Weizhu 31 Deng, Weihua 30 Brugnano, Luigi 30 Faou, Erwan 30 Schratz, Katharina 29 Auzinger, Winfried 28 Celledoni, Elena 28 Martín de Diego, David 28 Zhou, Zhi 26 Garrappa, Roberto 26 Iavernaro, Felice 26 Leok, Melvin 26 McLachlan, Robert I. 25 Conte, Dajana 25 Hochbruck, Marlis 25 Li, Jiyong 25 Tang, Yifa 25 You, Xiong 24 Cohen, David 24 Gong, Yuezheng 24 Owren, Brynjulf 24 Xiao, Aiguo 24 Zeng, Fanhai 23 Guglielmi, Nicola 23 Iserles, Arieh 23 Qiu, Wenlin 23 Sandu, Adrian 23 Sanz-Serna, Jesús María 23 Sun, Yajuan 22 Burrage, Kevin 22 D’Ambrosio, Raffaele 22 Koch, Othmar 22 Wang, Hong 22 Yan, Yubin 21 Thalhammer, Mechthild 21 Vecchio, Antonia 20 Ford, Neville J. 20 Fu, Yayun 20 Karniadakis, George Em 20 Kovacs, Balazs A. 20 Shi, Wei 19 Akrivis, Georgios D. 19 Ding, Xiaohua 19 Hong, Jialin 19 Jiang, Chaolong 19 Liu, Fawang 19 Paternoster, Beatrice 19 Sayas, Francisco-Javier 19 Schanz, Martin 18 Li, Changpin 18 Li, Dongfang 18 Mehrmann, Volker 18 Quispel, Gilles Reinout Willem 18 Vilmart, Gilles 18 Yang, Xuehua 18 Zhao, Jingjun 18 Zheng, Xiangcheng 17 Jiang, Yaolin 17 Kressner, Daniel 17 Liu, Kai 17 Liu, Yang 17 Ober-Blöbaum, Sina 17 Qiao, Leijie 17 Simeon, Bernd 17 Zhang, Haixiang 17 Zhang, Zhimin 16 Banjai, Lehel 16 Cai, Yongyong 16 Diele, Fasma 16 Günther, Michael 16 Jin, Bangti 16 Ju, Lili 16 Liu, Changying 16 Miyatake, Yuto 16 Mustapha, Kassem 16 Xu, Yang 16 Zhao, Xiaofei 15 Abdi, Ali 15 Bochev, M. A. 15 Cai, Jiaxiang 15 Hu, Dongdong 15 Kulikov, Gennady Yur’evich 15 Leyendecker, Sigrid 15 Li, Hong 15 Montijano, Juan Ignacio ...and 5,819 more Authors all top 5 Cited in 444 Serials 418 Journal of Computational Physics 349 Journal of Computational and Applied Mathematics 345 Applied Numerical Mathematics 204 BIT 190 Applied Mathematics and Computation 190 Journal of Scientific Computing 187 Numerische Mathematik 151 SIAM Journal on Scientific Computing 140 Computers & Mathematics with Applications 140 SIAM Journal on Numerical Analysis 134 Mathematics of Computation 122 Numerical Algorithms 107 Computer Methods in Applied Mechanics and Engineering 79 International Journal of Computer Mathematics 74 Mathematics and Computers in Simulation 71 Communications in Nonlinear Science and Numerical Simulation 70 Computer Physics Communications 66 Applied Mathematics Letters 61 Foundations of Computational Mathematics 61 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 59 Advances in Computational Mathematics 58 Numerical Methods for Partial Differential Equations 53 International Journal for Numerical Methods in Engineering 50 Engineering Analysis with Boundary Elements 43 SIAM Journal on Matrix Analysis and Applications 41 Linear Algebra and its Applications 38 Mathematical Methods in the Applied Sciences 38 Fractional Calculus & Applied Analysis 37 Calcolo 34 Computational and Applied Mathematics 32 Journal of Mathematical Analysis and Applications 32 Communications in Computational Physics 31 Journal of Computational Dynamics 30 Physica D 29 Numerical Linear Algebra with Applications 29 Discrete and Continuous Dynamical Systems. 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Académie des Sciences, Paris 10 International Journal of Applied and Computational Mathematics 9 Applicable Analysis 9 Communications in Mathematical Physics 9 Systems & Control Letters 9 Computational Mathematics and Mathematical Physics 9 Mathematical Problems in Engineering 9 Oberwolfach Reports 9 Science China. Mathematics 9 Journal of Applied Analysis and Computation 9 SIAM/ASA Journal on Uncertainty Quantification 9 Communications on Applied Mathematics and Computation 8 Automatica 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Networks and Heterogeneous Media 8 Discrete and Continuous Dynamical Systems. Series S 7 Archive for Rational Mechanics and Analysis 7 International Journal of Control 7 Journal of Fluid Mechanics 7 Journal of Statistical Physics 7 Applied Mathematics and Optimization 7 Journal of Complexity 7 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences ...and 344 more Serials all top 5 Cited in 57 Fields 4,516 Numerical analysis (65-XX) 1,829 Partial differential equations (35-XX) 926 Ordinary differential equations (34-XX) 632 Dynamical systems and ergodic theory (37-XX) 408 Mechanics of particles and systems (70-XX) 404 Integral equations (45-XX) 395 Fluid mechanics (76-XX) 329 Mechanics of deformable solids (74-XX) 299 Real functions (26-XX) 247 Probability theory and stochastic processes (60-XX) 234 Linear and multilinear algebra; matrix theory (15-XX) 226 Quantum theory (81-XX) 198 Statistical mechanics, structure of matter (82-XX) 152 Optics, electromagnetic theory (78-XX) 140 Biology and other natural sciences (92-XX) 136 Calculus of variations and optimal control; optimization (49-XX) 134 Systems theory; control (93-XX) 107 Operator theory (47-XX) 103 Differential geometry (53-XX) 100 Computer science (68-XX) 75 Difference and functional equations (39-XX) 70 Approximations and expansions (41-XX) 64 Operations research, mathematical programming (90-XX) 56 Statistics (62-XX) 47 Integral transforms, operational calculus (44-XX) 39 Geophysics (86-XX) 39 Information and communication theory, circuits (94-XX) 38 Harmonic analysis on Euclidean spaces (42-XX) 37 Global analysis, analysis on manifolds (58-XX) 35 Special functions (33-XX) 35 Classical thermodynamics, heat transfer (80-XX) 31 Combinatorics (05-XX) 31 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 27 Nonassociative rings and algebras (17-XX) 26 Associative rings and algebras (16-XX) 23 Functional analysis (46-XX) 21 Topological groups, Lie groups (22-XX) 17 General and overarching topics; collections (00-XX) 16 Relativity and gravitational theory (83-XX) 13 Astronomy and astrophysics (85-XX) 12 History and biography (01-XX) 7 Algebraic geometry (14-XX) 7 Potential theory (31-XX) 6 Manifolds and cell complexes (57-XX) 5 Functions of a complex variable (30-XX) 4 Commutative algebra (13-XX) 4 Category theory; homological algebra (18-XX) 4 Measure and integration (28-XX) 3 Geometry (51-XX) 2 Mathematical logic and foundations (03-XX) 2 Number theory (11-XX) 2 Several complex variables and analytic spaces (32-XX) 1 Group theory and generalizations (20-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-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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