Edit Profile (opens in new tab) Vilmart, Gilles Co-Author Distance Author ID: vilmart.gilles Published as: Vilmart, Gilles; Vilmart, G. External Links: MGP Documents Indexed: 40 Publications since 2006, including 2 Additional arXiv Preprints Co-Authors: 28 Co-Authors with 36 Joint Publications 861 Co-Co-Authors all top 5 Co-Authors 3 single-authored 16 Abdulle, Assyr 7 Chartier, Philippe 7 Zygalakis, Konstantinos C. 5 Hairer, Ernst 3 Laurent, Adrien 3 Lemou, Mohammed 2 Almuslimani, Ibrahim 2 Bai, Yun 2 Bertoli, Guillaume 2 Bréhier, Charles-Edouard 2 Méhats, Florian 1 Besse, Christophe 1 Castella, François 1 Chyba, Monique 1 Crouseilles, Nicolas 1 Descombes, Stéphane 1 Ducret, Verena 1 Durmus, Alain 1 Eftekhari, Armin 1 Gottwald, Georg A. 1 Huber, Martin E. 1 Makazaga, Joseba 1 Murua, Ander 1 Pavliotis, Grigorios A. 1 Perron, Karl 1 Roberts, Gareth O. 1 Sandoz, Antoine 1 Vandereycken, Bart all top 5 Serials 8 SIAM Journal on Scientific Computing 4 Mathematics of Computation 3 BIT 3 SIAM Journal on Numerical Analysis 3 Foundations of Computational Mathematics 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Computational Physics 2 Numerische Mathematik 1 IMA Journal of Numerical Analysis 1 International Journal for Numerical Methods in Engineering 1 The Annals of Applied Probability 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 International Journal of Computer Mathematics 1 Journal of Physics A: Mathematical and General 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Multiscale Modeling & Simulation 1 Discrete and Continuous Dynamical Systems. Series S 1 SIAM/ASA Journal on Uncertainty Quantification all top 5 Fields 38 Numerical analysis (65-XX) 17 Probability theory and stochastic processes (60-XX) 13 Partial differential equations (35-XX) 10 Dynamical systems and ergodic theory (37-XX) 8 Ordinary differential equations (34-XX) 4 Mechanics of deformable solids (74-XX) 3 Mechanics of particles and systems (70-XX) 1 Combinatorics (05-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Fluid mechanics (76-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 36 Publications have been cited 467 times in 316 Documents Cited by ▼ Year ▼ Algebraic structures of B-series. Zbl 1201.65124 Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles 54 2010 Splitting methods with complex times for parabolic equations. Zbl 1180.65106 Castella, F.; Chartier, P.; Descombes, S.; Vilmart, G. 46 2009 High order numerical approximation of the invariant measure of ergodic SDEs. Zbl 1310.65007 Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 28 2014 Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics. Zbl 1327.65015 Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 27 2015 High weak order methods for stochastic differential equations based on modified equations. Zbl 1246.65008 Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C. 22 2012 Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1282.65146 Abdulle, Assyr; Vilmart, Gilles 22 2014 A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems. Zbl 1251.65151 Abdulle, Assyr; Vilmart, Gilles 21 2012 Weak second-order explicit stabilized methods for stiff stochastic differential equations. Zbl 1281.65005 Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 20 2013 Numerical integrators based on modified differential equations. Zbl 1122.65059 Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles 19 2007 Optimal explicit stabilized integrator of weak order 1 for stiff and ergodic stochastic differential equations. Zbl 1392.65013 Abdulle, Assyr; Almuslimani, Ibrahim; Vilmart, Gilles 16 2018 Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete spacetime analysis. Zbl 1426.76208 Abdulle, Assyr; Vilmart, Gilles 15 2012 PIROCK: A swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise. Zbl 1297.65110 Abdulle, Assyr; Vilmart, Gilles 15 2013 Multi-revolution composition methods for highly oscillatory differential equations. Zbl 1307.65100 Chartier, Philippe; Makazaga, Joseba; Murua, Ander; Vilmart, Gilles 14 2014 Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1304.65245 Abdulle, Assyr; Bai, Yun; Vilmart, Gilles 13 2015 A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations. Zbl 07161200 Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles 13 2020 Postprocessed integrators for the high order integration of ergodic SDEs. Zbl 1327.65018 Vilmart, Gilles 11 2015 Fast Langevin based algorithm for MCMC in high dimensions. Zbl 1373.60053 Durmus, Alain; Roberts, Gareth O.; Vilmart, Gilles; Zygalakis, Konstantinos C. 10 2017 An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems. Zbl 1352.65462 Abdulle, A.; Bai, Y.; Vilmart, G. 9 2014 High order integrator for sampling the invariant distribution of a class of parabolic stochastic PDEs with additive space-time noise. Zbl 1346.60105 Bréhier, Charles-Edouard; Vilmart, Gilles 9 2016 Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems. Zbl 1336.74063 Abdulle, A.; Huber, M. E.; Vilmart, G. 9 2015 Drift-preserving numerical integrators for stochastic Poisson systems. Zbl 1480.65014 Cohen, David; Vilmart, Gilles 9 2022 Preprocessed discrete Moser-Veselov algorithm for the full dynamics of a rigid body. Zbl 1127.70002 Hairer, Ernst; Vilmart, Gilles 8 2006 Weak second order multirevolution composition methods for highly oscillatory stochastic differential equations with additive or multiplicative noise. Zbl 1320.65019 Vilmart, Gilles 8 2014 Mean-square \(A\)-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations. Zbl 1367.65011 Abdulle, A.; Vilmart, G.; Zygalakis, K. C. 8 2013 The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods. Zbl 1230.65122 Abdulle, Assyr; Vilmart, Gilles 6 2011 Reducing round-off errors in rigid body dynamics. Zbl 1140.70002 Vilmart, Gilles 5 2008 Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs. Zbl 1433.60078 Laurent, Adrien; Vilmart, Gilles 5 2020 Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds. Zbl 1487.60112 Laurent, Adrien; Vilmart, Gilles 5 2022 Strang splitting method for semilinear parabolic problems with inhomogeneous boundary conditions: a correction based on the flow of the nonlinearity. Zbl 1447.65058 Bertoli, Guillaume; Vilmart, Gilles 4 2020 Explicit stabilized integrators for stiff optimal control problems. Zbl 1460.49021 Almuslimani, Ibrahim; Vilmart, Gilles 4 2021 Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations. (Convergence accélérée vers l’équilibre et variance asymptotique réduite pour la dynamique de Langevin à l’aide de perturbations de Stratonovich.) Zbl 07066212 Abdulle, Assyr; Pavliotis, Grigorios A.; Vilmart, Gilles 3 2019 Asymptotic preserving numerical schemes for multiscale parabolic problems. (Schémas numériques Asymptotic Preserving pour les problèmes paraboliques multi-échelles.) Zbl 1387.65096 Crouseilles, Nicolas; Lemou, Mohammed; Vilmart, Gilles 2 2016 Multirevolution integrators for differential equations with fast stochastic oscillations. Zbl 1428.60097 Laurent, Adrien; Vilmart, Gilles 2 2020 Explicit stabilised gradient descent for faster strongly convex optimisation. Zbl 1462.90089 Eftekhari, Armin; Vandereycken, Bart; Vilmart, Gilles; Zygalakis, Konstantinos C. 2 2021 Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions. Zbl 1500.65059 Bertoli, Guillaume; Besse, Christophe; Vilmart, Gilles 2 2021 Highly oscillatory problems with time-dependent vanishing frequency. Zbl 1411.74046 Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles 1 2019 Drift-preserving numerical integrators for stochastic Poisson systems. Zbl 1480.65014 Cohen, David; Vilmart, Gilles 9 2022 Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds. Zbl 1487.60112 Laurent, Adrien; Vilmart, Gilles 5 2022 Explicit stabilized integrators for stiff optimal control problems. Zbl 1460.49021 Almuslimani, Ibrahim; Vilmart, Gilles 4 2021 Explicit stabilised gradient descent for faster strongly convex optimisation. Zbl 1462.90089 Eftekhari, Armin; Vandereycken, Bart; Vilmart, Gilles; Zygalakis, Konstantinos C. 2 2021 Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions. Zbl 1500.65059 Bertoli, Guillaume; Besse, Christophe; Vilmart, Gilles 2 2021 A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations. Zbl 07161200 Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles 13 2020 Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs. Zbl 1433.60078 Laurent, Adrien; Vilmart, Gilles 5 2020 Strang splitting method for semilinear parabolic problems with inhomogeneous boundary conditions: a correction based on the flow of the nonlinearity. Zbl 1447.65058 Bertoli, Guillaume; Vilmart, Gilles 4 2020 Multirevolution integrators for differential equations with fast stochastic oscillations. Zbl 1428.60097 Laurent, Adrien; Vilmart, Gilles 2 2020 Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations. (Convergence accélérée vers l’équilibre et variance asymptotique réduite pour la dynamique de Langevin à l’aide de perturbations de Stratonovich.) Zbl 07066212 Abdulle, Assyr; Pavliotis, Grigorios A.; Vilmart, Gilles 3 2019 Highly oscillatory problems with time-dependent vanishing frequency. Zbl 1411.74046 Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles 1 2019 Optimal explicit stabilized integrator of weak order 1 for stiff and ergodic stochastic differential equations. Zbl 1392.65013 Abdulle, Assyr; Almuslimani, Ibrahim; Vilmart, Gilles 16 2018 Fast Langevin based algorithm for MCMC in high dimensions. Zbl 1373.60053 Durmus, Alain; Roberts, Gareth O.; Vilmart, Gilles; Zygalakis, Konstantinos C. 10 2017 High order integrator for sampling the invariant distribution of a class of parabolic stochastic PDEs with additive space-time noise. Zbl 1346.60105 Bréhier, Charles-Edouard; Vilmart, Gilles 9 2016 Asymptotic preserving numerical schemes for multiscale parabolic problems. (Schémas numériques Asymptotic Preserving pour les problèmes paraboliques multi-échelles.) Zbl 1387.65096 Crouseilles, Nicolas; Lemou, Mohammed; Vilmart, Gilles 2 2016 Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics. Zbl 1327.65015 Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 27 2015 Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1304.65245 Abdulle, Assyr; Bai, Yun; Vilmart, Gilles 13 2015 Postprocessed integrators for the high order integration of ergodic SDEs. Zbl 1327.65018 Vilmart, Gilles 11 2015 Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems. Zbl 1336.74063 Abdulle, A.; Huber, M. E.; Vilmart, G. 9 2015 High order numerical approximation of the invariant measure of ergodic SDEs. Zbl 1310.65007 Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 28 2014 Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1282.65146 Abdulle, Assyr; Vilmart, Gilles 22 2014 Multi-revolution composition methods for highly oscillatory differential equations. Zbl 1307.65100 Chartier, Philippe; Makazaga, Joseba; Murua, Ander; Vilmart, Gilles 14 2014 An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems. Zbl 1352.65462 Abdulle, A.; Bai, Y.; Vilmart, G. 9 2014 Weak second order multirevolution composition methods for highly oscillatory stochastic differential equations with additive or multiplicative noise. Zbl 1320.65019 Vilmart, Gilles 8 2014 Weak second-order explicit stabilized methods for stiff stochastic differential equations. Zbl 1281.65005 Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 20 2013 PIROCK: A swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise. Zbl 1297.65110 Abdulle, Assyr; Vilmart, Gilles 15 2013 Mean-square \(A\)-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations. Zbl 1367.65011 Abdulle, A.; Vilmart, G.; Zygalakis, K. C. 8 2013 High weak order methods for stochastic differential equations based on modified equations. Zbl 1246.65008 Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C. 22 2012 A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems. Zbl 1251.65151 Abdulle, Assyr; Vilmart, Gilles 21 2012 Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete spacetime analysis. Zbl 1426.76208 Abdulle, Assyr; Vilmart, Gilles 15 2012 The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods. Zbl 1230.65122 Abdulle, Assyr; Vilmart, Gilles 6 2011 Algebraic structures of B-series. Zbl 1201.65124 Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles 54 2010 Splitting methods with complex times for parabolic equations. Zbl 1180.65106 Castella, F.; Chartier, P.; Descombes, S.; Vilmart, G. 46 2009 Reducing round-off errors in rigid body dynamics. Zbl 1140.70002 Vilmart, Gilles 5 2008 Numerical integrators based on modified differential equations. Zbl 1122.65059 Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles 19 2007 Preprocessed discrete Moser-Veselov algorithm for the full dynamics of a rigid body. Zbl 1127.70002 Hairer, Ernst; Vilmart, Gilles 8 2006 all cited Publications top 5 cited Publications all top 5 Cited by 418 Authors 30 Abdulle, Assyr 24 Vilmart, Gilles 17 Chartier, Philippe 10 Blanes, Sergio 9 Lemou, Mohammed 9 Zhao, Xiaofei 8 Bruned, Yvain 8 Casas, Fernando 8 D’Ambrosio, Raffaele 8 Ebrahimi-Fard, Kurusch 8 Méhats, Florian 8 Zygalakis, Konstantinos C. 7 Bréhier, Charles-Edouard 7 Hong, Jialin 6 Crouseilles, Nicolas 6 Laurent, Adrien 6 Manchon, Dominique 6 McLachlan, Robert I. 6 Shang, Xiaocheng 5 Bai, Yun 5 Chen, Chuchu 5 Escorihuela-Tomàs, Alejandro 5 Huber, Martin E. 5 Murua, Ander 5 Sanz-Serna, Jesús María 4 Almuslimani, Ibrahim 4 Bogfjellmo, Geir 4 Burrage, Kevin 4 De Souza, Giacomo Rosilho 4 Di Giovacchino, Stefano 4 Kleefeld, Andreas 4 Munthe-Kaas, Hans Z. 4 Ostermann, Alexander 4 Seydaoğlu, Muaz 4 Stoltz, Gabriel 4 Tang, Xiao 4 Thalhammer, Mechthild 4 Xiao, Aiguo 3 Besse, Christophe 3 Curry, Charles 3 Dikhaminjia, Nana 3 Hairer, Martin 3 Hansen, Eskil 3 Koch, Othmar 3 Komori, Yoshio 3 Kvaerno, Anne 3 Leimkuhler, Benedict J. 3 Li, Qin 3 Lu, Jianfeng 3 Majka, Mateusz B. 3 Montijano, Juan Ignacio 3 Paternoster, Beatrice 3 Pereyra, Marcelo 3 Pollock, Sara 3 Rández, Luis 3 Rogava, Jemal L. 3 Scalone, Carmela 3 Schmeding, Alexander 3 Schratz, Katharina 3 Sun, Liying 3 Szpruch, Lukasz 3 Tsiklauri, Mikheil 3 Verdier, Olivier 3 Wang, Xu 3 Wright, Stephen J. 3 Zhu, Yunrong 2 Arjmand, Doghonay 2 Auzinger, Winfried 2 Bader, Philipp 2 Bailleul, Ismaël F. 2 Bernier, Joackim 2 Bi, Chunjia 2 Biscay, Rolando J. 2 Blumenthal, Adrian 2 Calvo, Manuel 2 Chen, Shi 2 Chung, Tsz Shun Eric 2 Dahmen, Rafael 2 Debrabant, Kristian 2 Durmus, Alain 2 Eftekhari, Armin 2 Einkemmer, Lukas 2 Ekre, Fredrik 2 Engquist, Bjorn E. 2 Erdoğan, Utku 2 Frénod, Emmanuel 2 González, Cesáreo 2 Guo, Liming 2 Hairer, Ernst 2 Henning, Patrick 2 Hoang, Viet Ha 2 Hochbruck, Marlis 2 Hofstätter, Harald 2 Jackiewicz, Zdzislaw 2 Jänicke, Ralf 2 Keil, Tim 2 Kock, Joachim 2 Kropat, Erik 2 Laburta, María Pilar 2 Larsson, Fredrik ...and 318 more Authors all top 5 Cited in 97 Serials 32 Journal of Computational Physics 19 BIT 16 Journal of Computational and Applied Mathematics 15 SIAM Journal on Scientific Computing 14 Applied Numerical Mathematics 13 Mathematics of Computation 13 Numerische Mathematik 12 Multiscale Modeling & Simulation 11 Foundations of Computational Mathematics 10 SIAM Journal on Numerical Analysis 8 Numerical Algorithms 7 Journal of Scientific Computing 6 Discrete and Continuous Dynamical Systems. Series B 6 Discrete and Continuous Dynamical Systems. Series S 5 Oberwolfach Reports 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 5 Journal of Computational Dynamics 4 Advances in Computational Mathematics 3 Computers & Mathematics with Applications 3 Applied Mathematics and Computation 3 Numerical Methods for Partial Differential Equations 3 International Journal of Computer Mathematics 3 Journal of Machine Learning Research (JMLR) 3 SIAM Journal on Imaging Sciences 3 Statistics and Computing 3 Forum of Mathematics, Sigma 2 Computer Methods in Applied Mechanics and Engineering 2 International Journal for Numerical Methods in Engineering 2 Mathematics and Computers in Simulation 2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 Stochastic Processes and their Applications 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 SIAM Journal on Optimization 2 Computational and Applied Mathematics 2 Optimization Methods & Software 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Communications in Computational Physics 2 Advances in Applied Mathematics and Mechanics 2 Numerical Algebra, Control and Optimization 2 Stochastic and Partial Differential Equations. Analysis and Computations 1 Acta Mechanica 1 Advances in Applied Probability 1 Communications in Mathematical Physics 1 Computer Physics Communications 1 Mathematical Methods in the Applied Sciences 1 Physics Letters. A 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 The Annals of Statistics 1 Bulletin of the London Mathematical Society 1 Inventiones Mathematicae 1 Journal of Algebra 1 Journal of the American Statistical Association 1 Journal of Differential Equations 1 Journal of the London Mathematical Society. Second Series 1 Journal of the Mathematical Society of Japan 1 Mathematische Annalen 1 Numerical Functional Analysis and Optimization 1 Advances in Applied Mathematics 1 Journal of Computational Mathematics 1 Journal of Complexity 1 Computational Mechanics 1 Applied Mathematics Letters 1 SIAM Journal on Matrix Analysis and Applications 1 The Annals of Applied Probability 1 European Journal of Operational Research 1 SIAM Review 1 Celestial Mechanics and Dynamical Astronomy 1 Journal of Nonlinear Science 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Potential Analysis 1 Journal of Mathematical Sciences (New York) 1 Georgian Mathematical Journal 1 Electronic Journal of Probability 1 Discrete and Continuous Dynamical Systems 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Journal of the European Mathematical Society (JEMS) 1 Communications in Nonlinear Science and Numerical Simulation 1 Mathematical Modelling and Analysis 1 Journal of Numerical Mathematics 1 International Journal of Computational Methods 1 International Journal of Geometric Methods in Modern Physics 1 Acta Numerica 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Journal of Noncommutative Geometry 1 Networks and Heterogeneous Media 1 Electronic Journal of Statistics 1 Journal of Geometric Mechanics 1 Forum of Mathematics, Pi 1 Mathematical Sciences 1 SIAM/ASA Journal on Uncertainty Quantification 1 Annales de l’Institut Henri Poincaré D. Combinatorics, Physics and their Interactions 1 Journal de l’École Polytechnique – Mathématiques 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 SIAM Journal on Mathematics of Data Science all top 5 Cited in 40 Fields 256 Numerical analysis (65-XX) 100 Partial differential equations (35-XX) 94 Probability theory and stochastic processes (60-XX) 39 Dynamical systems and ergodic theory (37-XX) 37 Ordinary differential equations (34-XX) 22 Associative rings and algebras (16-XX) 19 Mechanics of deformable solids (74-XX) 18 Statistical mechanics, structure of matter (82-XX) 14 Computer science (68-XX) 14 Fluid mechanics (76-XX) 12 Combinatorics (05-XX) 11 Statistics (62-XX) 11 Mechanics of particles and systems (70-XX) 10 Approximations and expansions (41-XX) 10 Quantum theory (81-XX) 8 Operations research, mathematical programming (90-XX) 6 Topological groups, Lie groups (22-XX) 6 Functional analysis (46-XX) 5 General and overarching topics; collections (00-XX) 5 Nonassociative rings and algebras (17-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Operator theory (47-XX) 4 Systems theory; control (93-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Category theory; homological algebra (18-XX) 3 Optics, electromagnetic theory (78-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral equations (45-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Biology and other natural sciences (92-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Special functions (33-XX) 1 Differential geometry (53-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year