Edit Profile (opens in new tab) Sanz-Serna, Jesús María Co-Author Distance Author ID: sanz-serna.jesus-maria Published as: Sanz-Serna, J. M.; Sanz-Serna, Jesús María; Sanz Serna, J. M.; Sanz Serna, Jesus; Sanz-Serna, J.-M.; Sanz-Serna, Chus (J. M.); Sanz-Serna, Jesus Maria; Sanz-Serna, Jesus-Maria; Sanz-Serna, Jesus M.; Sanz-Serna, Jesús M.; Sanz-Serna, J. more...less Homepage: http://sanzserna.org/ External Links: MGP · ORCID · Wikidata · Google Scholar · dblp · IdRef Documents Indexed: 169 Publications since 1976, including 6 Books and 7 Additional arXiv Preprints 2 Contributions as Editor · 2 Further Contributions Reviewing Activity: 76 Reviews Biographic References: 1 Publication Co-Authors: 69 Co-Authors with 137 Joint Publications 1,552 Co-Co-Authors all top 5 Co-Authors 33 single-authored 17 Murua, Ander 16 Calvo, M. P. 9 Christie, Ian 9 Verwer, Jan G. 7 Abia, Luis María 7 Chartier, Philippe 7 de Frutos, Javier 5 López-marcos, Miguel Ángel 5 Stuart, Andrew M. 5 Zygalakis, Konstantinos C. 4 Casas, Fernando 4 Griffiths, David F. 4 Ortega, Tomás 4 Skeel, Robert D. 3 Akhmatskaya, Elena 3 Beskos, Alexandros 3 Fernández-Pendás, Mario 3 García-Archilla, Bosco 3 Hairer, Ernst 3 Iserles, Arieh 3 Larsson, Stig 3 McLeod, Robin J. Y. 3 Palencia, Cesar 3 Vadillo, Fernando 3 Zhu, Beibei 2 Alamo, A. 2 Blanes, Sergio 2 Blom, Joke G. 2 Bou-Rabee, Nawaf M. 2 Campos, Cédric Martínez 2 Cano, Begoña 2 Dobson, Paul W. 2 Duran, Angel 2 Eirola, Timo 2 Ganser, Gary H. 2 Koch, Per Erik 2 López-Marcos, Juan Carlos 2 Manoranjan, Valipuram S. 2 Marquina, Antonio 2 Nørsett, Syvert Paul 2 Paz Calvo, Mari 2 Pillai, Natesh S. 2 Roberts, Gareth O. 2 Shaw, Luke 2 Tourigny, Yves 1 Adams, Ryan Prescott 1 Altmann, Yoann 1 Anaya-Izquierdo, Karim Alejandro 1 Archambeau, Cédric 1 Ariel, Gil 1 Barthelmé, Simon 1 Beffy, Magali 1 Beyn, Wolf-Jürgen 1 Bhadra, Anindya 1 Bornn, Luke 1 Bouchard, Guillaume 1 Boys, Richard J. 1 Butcher, John C. 1 Calderhead, Ben 1 Campbell, David A. 1 Celledoni, Elena 1 Chen, Yanjiun 1 Chin, Siu A. 1 Chopin, Nicolas 1 Christie, Mike 1 Coolen, Anthony C. C. 1 Cornebise, Julien 1 Cox, David Roxbee 1 Critchley, Frank 1 Dieci, Luca 1 Doblaré, Manuel 1 Dopico, Froilán M. 1 Doucet, Arnaud 1 Draper, David 1 Dryden, Ian L. 1 Durán Martín, Angel 1 Eguchi, Shinto 1 Fairweather, Graeme 1 Fearnhead, Paul 1 Filippone, Maurizio 1 Friel, Nial 1 Gelman, Andrew 1 Girolami, Mark A. 1 Golightly, Andrew 1 Griffin, Jim E. 1 Gripton, Adam 1 Guerrera, Thiago 1 Guglielmi, Nicola 1 Guillas, Serge 1 Gutenkunst, Ryan 1 Haario, Heikki 1 Higham, Desmond J. 1 Hochbruck, Marlis 1 Holmes, Christopher C. 1 Honkela, Antti 1 Hundsdorfer, Willem H. 1 Husmeier, Dirk 1 Ikeda, Shiro 1 Jacob, Pierre E. 1 Jasra, Ajay ...and 56 more Co-Authors all top 5 Serials 18 Journal of Computational Physics 14 IMA Journal of Numerical Analysis 11 SIAM Journal on Numerical Analysis 10 Numerische Mathematik 8 Applied Numerical Mathematics 8 SIAM Journal on Scientific Computing 7 Mathematics of Computation 5 Foundations of Computational Mathematics 4 BIT 3 La Gaceta de la Real Sociedad Matemática Española 2 Computer Methods in Applied Mechanics and Engineering 2 Archiv der Mathematik 2 Computing 2 International Journal for Numerical Methods in Engineering 2 SIAM Journal on Scientific and Statistical Computing 2 Discrete and Continuous Dynamical Systems 2 Applied Mathematics and Nonlinear Sciences 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 Nonlinearity 1 Applied Mathematics and Computation 1 Collectanea Mathematica 1 Consejo Superior de Investigaciones Cientificas. Instituto ”Jorge Juan”. Gaceta Matematica. 1a Serie 1 Journal of Approximation Theory 1 Journal of Computational and Applied Mathematics 1 Journal of Differential Equations 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Physica D 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Communications in Applied Numerical Methods 1 Numerical Methods for Partial Differential Equations 1 The Annals of Applied Probability 1 SIAM Journal on Applied Mathematics 1 SIAM Review 1 Stochastic Processes and their Applications 1 Bernoulli 1 Journal of the Royal Statistical Society. Series B. Statistical Methodology 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Machine Learning Research (JMLR) 1 Stochastics and Dynamics 1 Communications on Pure and Applied Analysis 1 Multiscale Modeling & Simulation 1 Acta Numerica 1 Oberwolfach Reports 1 BIT. Nordisk Tidskrift for Informationsbehandling 1 Applied Mathematics and Mathematical Computation 1 Lecture Notes in Mathematics 1 Monografías y Memorias de Matemáticas 1 Statistics and Computing all top 5 Fields 141 Numerical analysis (65-XX) 52 Ordinary differential equations (34-XX) 44 Partial differential equations (35-XX) 44 Dynamical systems and ergodic theory (37-XX) 28 Mechanics of particles and systems (70-XX) 12 Probability theory and stochastic processes (60-XX) 10 Quantum theory (81-XX) 5 Functional analysis (46-XX) 5 Statistics (62-XX) 5 Fluid mechanics (76-XX) 3 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 3 Associative rings and algebras (16-XX) 3 Operations research, mathematical programming (90-XX) 3 Systems theory; control (93-XX) 2 Approximations and expansions (41-XX) 2 Integral equations (45-XX) 2 Operator theory (47-XX) 2 Computer science (68-XX) 2 Mechanics of deformable solids (74-XX) 2 Biology and other natural sciences (92-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 General topology (54-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 142 Publications have been cited 3,197 times in 2,067 Documents Cited by ▼ Year ▼ Numerical Hamiltonian problems. Zbl 0816.65042 Sanz-Serna, J. M.; Calvo, M. P. 435 1994 Riemann manifold Langevin and Hamiltonian Monte Carlo methods. With discussion and authors’ reply. Zbl 1411.62071 Girolami, Mark; Calderhead, Ben 248 2011 Runge-Kutta schemes for Hamiltonian systems. Zbl 0655.70013 Sanz-Serna, J. M. 161 1988 Symplectic integrators for Hamiltonian problems: An overview. Zbl 0762.65043 Sanz-Serna, J. M. 117 1992 On polynomials orthogonal with respect to certain Sobolev inner products. Zbl 0734.42016 Iserles, Arieh; Koch, P. E.; Nørsett, Syvert P.; Sanz-Serna, J. M. 112 1991 A numerical method for a partial integro-differential equation. Zbl 0643.65098 Sanz-Serna, J. M. 90 1988 Long-time-step methods for oscillatory differential equations. Zbl 0927.65143 García-Archilla, B.; Sanz-Serna, J. M.; Skeel, R. D. 89 1999 Methods for the numerical solution of the nonlinear Schrödinger equation. Zbl 0555.65061 Sanz-Serna, J. M. 79 1984 Product approximation for non-linear problems in the finite element method. Zbl 0469.65072 Christie, I.; Griffiths, D. F.; Mitchell, A. R.; Sanz-Serna, J. M. 76 1981 Conservative and nonconservative schemes for the solution of the nonlinear Schrödinger equation. Zbl 0593.65087 Sanz-Serna, J. M.; Verwer, J. G. 75 1986 Optimal tuning of the hybrid Monte Carlo algorithm. Zbl 1287.60090 Beskos, Alexandros; Pillai, Natesh; Roberts, Gareth; Sanz-Serna, Jesus-Maria; Stuart, Andrew 66 2013 Convergence and order reduction of Runge-Kutta schemes applied to evolutionary problems in partial differential equations. Zbl 0589.65069 Sanz-Serna, J. M.; Verwer, J. G.; Hundsdorfer, W. H. 63 1987 Petrov-Galerkin methods for nonlinear dispersive waves. Zbl 0451.65086 Sanz-Serna, J. M.; Christie, I. 58 1981 The development of variable-step symplectic integrators, with application to the two-body problem. Zbl 0785.65083 Calvo, M. P.; Sanz-Serna, J. M. 54 1993 Order conditions for canonical Runge-Kutta schemes. Zbl 0785.65085 Sanz-Serna, J. M.; Abia, L. 48 1991 The numerical integration of relative equilibrium solutions. The nonlinear Schrödinger equation. Zbl 0954.65087 Durán, A.; Sanz-Serna, J. M. 45 2000 Hybrid Monte Carlo on Hilbert spaces. Zbl 1235.60091 Beskos, A.; Pinski, F. J.; Sanz-Serna, J. M.; Stuart, A. M. 45 2011 On the scope of the method of modified equations. Zbl 0613.65079 Griffiths, D. F.; Sanz-Serna, J. M. 42 1986 Convergence of method of lines approximations to partial differential equations. Zbl 0546.65064 Verwer, J. G.; Sanz-Serna, J. M. 40 1984 Soliton and antisoliton interactions in the “good” Boussinesq equation. Zbl 0673.35089 Manoranjan, V. S.; Ortega, T.; Sanz-Serna, J. M. 39 1988 Randomized Hamiltonian Monte Carlo. Zbl 1373.60129 Bou-Rabee, Nawaf; Sanz-Serna, Jesús María 38 2017 Stability and convergence in numerical analysis. III: Linear investigation of nonlinear stability. Zbl 0695.65042 López-Marcos, J. C.; Sanz-Serna, J. M. 34 1988 An easily implementable fourth-order method for the time integration of wave problems. Zbl 0761.65074 de Frutos, J.; Sanz-Serna, J. M. 34 1992 High-order symplectic Runge-Kutta-Nyström methods. Zbl 0787.65056 Calvo, M. P.; Sanz-Serna, J. M. 34 1993 Nonlinear stability and convergence of finite-difference methods for the ”good” Boussinesq equation. Zbl 0749.65082 Ortega, T.; Sanz-Serna, J. M. 33 1990 Accuracy and conservation properties in numerical integration: The case of the Korteweg-de Vries equation. Zbl 0876.65068 de Frutos, J.; Sanz-Serna, J. M. 33 1997 Pseudospectral method for the ”good” Boussinesq equation. Zbl 0735.65089 de Frutos, J.; Ortega, T.; Sanz-Serna, J. M. 31 1991 Symplectic Runge-Kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. Zbl 1339.65243 Sanz-Serna, J. M. 31 2016 An explicit finite-difference scheme with exact conservation properties. Zbl 0484.65062 Sanz-Serna, J. M. 30 1982 Modulated Fourier expansions and heterogeneous multiscale methods. Zbl 1167.65393 Sanz-Serna, J. M. 30 2009 Geometric integrators and the Hamiltonian Monte Carlo method. Zbl 1431.65004 Bou-Rabee, Nawaf; Sanz-Serna, J. M. 30 2018 A method for the integration in time of certain partial differential equations. Zbl 0514.65085 Sanz-Serna, J. M.; Manoranjan, V. S. 27 1983 Higher-order averaging, formal series and numerical integration. I: B-series. Zbl 1211.34052 Chartier, P.; Murua, A.; Sanz-Serna, J. M. 27 2010 Error growth in the numerical integration of periodic orbits, with application to Hamiltonian and reversible systems. Zbl 0889.65081 Cano, B.; Sanz-Serna, J. M. 26 1997 Ergodicity of dissipative differential equations subject to random impulses. Zbl 0934.34047 Sanz-Serna, J. M.; Stuart, A. M. 25 1999 Partitioned Runge-Kutta methods for separable Hamiltonian problems. Zbl 0777.65042 Abia, L.; Sanz-Serna, J. M. 25 1993 On simple moving grid methods for one-dimensional evolutionary partial differential equations. Zbl 0645.65060 Blom, J. G.; Sanz-Serna, J. M.; Verwer, J. G. 24 1988 A finite difference scheme for the \(K(2,2)\) compacton equation. Zbl 0840.65090 de Frutos, J.; López-Marcos, M. A.; Sanz-Serna, J. M. 24 1995 Split-step spectral schemes for nonlinear Dirac systems. Zbl 0675.65131 de Frutos, J.; Sanz-Serna, J. M. 23 1989 Symplectic methods based on decompositions. Zbl 0889.65082 Araújo, A. L.; Murua, A.; Sanz-Serna, J. M. 23 1997 An unconventional symplectic integrator of W. Kahan. Zbl 0815.65090 Sanz-Serna, J. M. 23 1994 A simple adaptive technique for nonlinear wave problems. Zbl 0653.65087 Sanz-Serna, J. M.; Christie, I. 22 1986 Order conditions for numerical integrators obtained by composing simpler integrators. Zbl 0946.65056 Murua, A.; Sanz-Serna, J. M. 21 1999 Orthogonality and approximation in a Sobolev space. Zbl 0749.41030 Iserles, Arieh; Sanz-Serna, J. M.; Koch, P. E.; Nørsett, Syvert P. 21 1990 Mollified impulse methods for highly oscillatory differential equations. Zbl 1169.65081 Sanz-Serna, J. M. 20 2008 Higher-order averaging, formal series and numerical integration. III: Error bounds. Zbl 1322.34057 Chartier, P.; Murua, A.; Sanz-Serna, J. M. 19 2015 Stability and convergence at the PDE/stiff ODE interface. Zbl 0671.65078 Sanz-Serna, J. M.; Verwer, J. G. 18 1989 Numerical stroboscopic averaging for ODEs and DAEs. Zbl 1223.65063 Calvo, M. P.; Chartier, Ph.; Murua, A.; Sanz-Serna, J. M. 18 2011 Geometric integration. Zbl 0886.65074 Sanz-Serna, J. M. 18 1997 Order conditions for canonical Runge-Kutta-Nyström methods. Zbl 0802.65089 Calvo, M. P.; Sanz-Serna, J. M. 18 1992 Numerical integrators for the hybrid Monte Carlo method. Zbl 1312.65209 Blanes, Sergio; Casas, Fernando; Sanz-Serna, J. M. 18 2014 The numerical integration of Hamiltonian systems. Zbl 0766.65058 Sanz-Serna, J. M. 17 1992 Higher-order averaging, formal series and numerical integration. II: The quasi-periodic case. Zbl 1257.34031 Chartier, P.; Murua, A.; Sanz-Serna, J. M. 17 2012 A definition of stability for nonlinear problems. Zbl 0679.65039 López-Marcos, J. C.; Sanz-Serna, J. M. 16 1988 Canonical \(B\)-series. Zbl 0791.65049 Calvo, M. P.; Sanz-Serna, J. M. 16 1994 A formal series approach to averaging: exponentially small error estimates. Zbl 1246.34043 Chartier, Philippe; Murua, Ander; Sanz-Serna, Jesús María 16 2012 An adaptive moving grid method for one-dimensional systems of partial differential equations. Zbl 0675.65098 Verwer, J. G.; Blom, J. G.; Sanz-Serna, J. M. 15 1989 Error growth in the numerical integration of periodic orbits by multistep methods, with application to reversible systems. Zbl 0905.65082 Cano, B.; Sanz-Serna, J. M. 15 1998 Convergence of methods for the numerical solution of the Korteweg-de Vries equation. Zbl 0455.65082 Kuo, Pen-Yu; Sanz-Serna, J. M. 15 1981 A general equivalence theorem in the theory of discretization methods. Zbl 0599.65034 Sanz-Serna, J. M.; Palencia, C. 14 1985 Word series for dynamical systems and their numerical integrators. Zbl 1369.34022 Murua, A.; Sanz-Serna, J. M. 14 2017 Markov chain Monte Carlo and numerical differential equations. Zbl 1318.65007 Sanz-Serna, J. M. 14 2014 A Galerkin method for a nonlinear integro-differential wave system. Zbl 0525.73089 Christie, I.; Sanz-Serna, J. M. 13 1984 Equilibria of Runge-Kutta methods. Zbl 0693.65047 Hairer, E.; Iserles, A.; Sanz-Serna, J. M. 13 1990 Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods. Zbl 0735.65048 Eirola, T.; Sanz-Serna, J. M. 13 1992 Modified equations for ODEs. Zbl 0807.65074 Calvo, M. P.; Murua, A.; Sanz-Serna, J. M. 13 1994 Computing normal forms and formal invariants of dynamical systems by means of word series. Zbl 1334.34087 Murua, A.; Sanz-Serna, J. M. 13 2016 Cheap enhancement of symplectic integrators. Zbl 0843.65050 López-Marcos, M. A.; Sanz-Serna, J. M.; Skeel, R. D. 12 1996 A Hamiltonian, explicit algorithm with spectral accuracy for the ‘good’ Boussinesq system. Zbl 0728.76072 de Frutos, J.; Ortega, T.; Sanz-Serna, J. M. 12 1990 Two topics in nonlinear stability. Zbl 0746.65069 Sanz-Serna, J. M. 12 1991 A note on uniform in time error estimates for approximations to reaction- diffusion equations. Zbl 0781.65080 Sanz-Serna, J. M.; Stuart, A. M. 12 1992 Explicit symplectic integrators using Hessian-vector products. Zbl 0868.65056 López-Marcos, M. A.; Sanz-Serna, J. M.; Skeel, Robert D. 12 1997 The behavior of finite element solutions of semilinear parabolic problems near stationary points. Zbl 0811.65072 Larsson, S.; Sanz-Serna, J.-M. 12 1994 Remarks on methods for the computation of boundary-element integrals by co-ordinate transformation. Zbl 0693.65012 Sanz-Serna, J.; Doblare, M.; Alarcon, E. 11 1990 A finite difference formula for the discretization of \(d^ 3/dx^ 3\) on nonuniform grids. Zbl 0727.65011 Garcia-Archilla, B.; Sanz-Serna, J. M. 11 1991 A technique for studying strong and weak local errors of splitting stochastic integrators. Zbl 1353.65004 Alamo, A.; Sanz-Serna, J. M. 11 2016 Interpolation of the coefficients in nonlinear elliptic Galerkin procedures. Zbl 0542.65042 Sanz-Serna, J. M.; Abia, L. 10 1984 The numerical integration of relative equilibrium solutions. Geometric theory. Zbl 0913.65069 Durán, A.; Sanz-Serna, J. M. 10 1998 The numerical study of blowup with application to a nonlinear Schrödinger equation. Zbl 0761.65099 Tourigny, Y.; Sanz-Serna, J. M. 10 1992 Variable steps for symplectic integrators. Zbl 0795.65049 Calvo, M. P.; Sanz-Serna, J. M. 10 1992 Numerical Hamiltonian problems. Reprint of the 1994 original published by Chapman & Hall. Zbl 1418.65002 Sanz-Serna, Jesús María; Calvo, M. P. 10 2018 Convergence analysis of one-step schemes in the method of lines. Zbl 0671.65077 Sanz-Serna, J. M.; Verwer, J. G. 9 1989 Equivalence theorems for incomplete spaces: An appraisal. Zbl 0559.65033 Palencia, C.; Sanz-Serna, J. M. 9 1984 The non-existence of symplectic multi-derivative Runge-Kutta methods. Zbl 0816.65043 Hairer, E.; Murua, A.; Sanz-Serna, J. M. 9 1994 Studies in numerical nonlinear instability. I. Why do leapfrog schemes go unstable? Zbl 0612.65052 Sanz-Serna, J. M. 9 1985 The number of conditions for a Runge-Kutta method to have effective order \(p\). Zbl 0867.65039 Butcher, J. C.; Sanz-Serna, J. M. 9 1996 Symplectic Runge-Kutta and related methods: Recent results. Zbl 0779.58019 Sanz-Serna, J. M. 9 1992 Extra chance generalized hybrid Monte Carlo. Zbl 1352.65007 Campos, Cédric M.; Sanz-Serna, J. M. 9 2015 An extension of the Lax-Richtmyer theory. Zbl 0523.65067 Palencia, C.; Sanz-Serna, J. M. 8 1984 Heterogeneous multiscale methods for mechanical systems with vibrations. Zbl 1241.65071 Calvo, M. P.; Sanz-Serna, J. M. 8 2010 A shadowing result with applications to finite element approximation of reaction-diffusion equations. Zbl 0913.65079 Larsson, Stig; Sanz-Serna, J.-M. 8 1999 Variable step implementation of geometric integrators. Zbl 0930.65136 Calvo, M. P.; López-Marcos, M. A.; Sanz-Serna, J. M. 8 1998 A study of the recursion \(y_{n+1}=y_ n+\tau y^ m_ n\). Zbl 0599.65086 Sanz-Serna, J. M.; Verwer, J. G. 8 1986 Numerical ordinary differential equations vs. dynamical systems. Zbl 0764.34009 Sanz-Serna, J. M. 8 1992 Vibrational resonance: a study with high-order word-series averaging. Zbl 1432.34058 Murua, A.; Sanz-Serna, J. M. 8 2016 Adaptive multi-stage integrators for optimal energy conservation in molecular simulations. Zbl 1422.65447 Fernández-Pendás, Mario; Akhmatskaya, Elena; Sanz-Serna, J. M. 7 2016 Palindromic 3-stage splitting integrators, a roadmap. Zbl 1378.65154 Campos, Cédric M.; Sanz-Serna, J. M. 7 2017 A multiscale technique for finding slow manifolds of stiff mechanical systems. Zbl 1332.65100 Ariel, G.; Sanz-Serna, J. M.; Tsai, R. 7 2012 Studies in numerical nonlinear instability. III. Augmented Hamiltonian systems. Zbl 0632.65129 Sanz-Serna, J. M.; Vadillo, F. 6 1987 Nonlinear instability, the dynamic approach. Zbl 0651.65060 Sanz-Serna, J. M.; Vadillo, F. 6 1986 Split Hamiltonian Monte Carlo revisited. Zbl 1496.62006 Casas, Fernando; Sanz-Serna, Jesús María; Shaw, Luke 1 2022 Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations. Zbl 07626757 Sanz-Serna, Jesus Maria; Zygalakis, Konstantinos C. 6 2021 The connections between Lyapunov functions for some optimization algorithms and differential equations. Zbl 1467.65070 Sanz Serna, J. M.; Zygalakis, K. C. 5 2021 HMC: reducing the number of rejections by not using leapfrog and some results on the acceptance rate. Zbl 07505916 Calvo, M. P.; Sanz-Alonso, D.; Sanz-Serna, J. M. 3 2021 Symmetrically processed splitting integrators for enhanced Hamiltonian Monte Carlo sampling. Zbl 1487.65006 Blanes, S.; Calvo, M. P.; Casas, F.; Sanz-Serna, J. M. 1 2021 Contractivity of Runge-Kutta methods for convex gradient systems. Zbl 1451.65092 Sanz Serna, J. M.; Zygalakis, K. C. 3 2020 High-order stroboscopic averaging methods for highly oscillatory delay problems. Zbl 1445.65023 Calvo, M. P.; Sanz-Serna, J. M.; Zhu, Beibei 2 2020 Word combinatorics for stochastic differential equations: splitting integrators. Zbl 1476.60092 Alamo, A.; Sanz-Serna, J. M. 4 2019 A stroboscopic averaging algorithm for highly oscillatory delay problems. Zbl 1464.65071 Sanz-Serna, J. M.; Zhu, Beibei 1 2019 Geometric integrators and the Hamiltonian Monte Carlo method. Zbl 1431.65004 Bou-Rabee, Nawaf; Sanz-Serna, J. M. 30 2018 Numerical Hamiltonian problems. Reprint of the 1994 original published by Chapman & Hall. Zbl 1418.65002 Sanz-Serna, Jesús María; Calvo, M. P. 10 2018 Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods. Zbl 1416.65517 Radivojević, Tijana; Fernández-Pendás, Mario; Sanz-Serna, Jesús María; Akhmatskaya, Elena 5 2018 Hopf algebra techniques to handle dynamical systems and numerical integrators. Zbl 1409.37082 Murua, Ander; Sanz-Serna, Jesús M. 3 2018 Randomized Hamiltonian Monte Carlo. Zbl 1373.60129 Bou-Rabee, Nawaf; Sanz-Serna, Jesús María 38 2017 Word series for dynamical systems and their numerical integrators. Zbl 1369.34022 Murua, A.; Sanz-Serna, J. M. 14 2017 Palindromic 3-stage splitting integrators, a roadmap. Zbl 1378.65154 Campos, Cédric M.; Sanz-Serna, J. M. 7 2017 Erratum to: “Higher-order averaging, formal series and numerical integration. II: The quasi-periodic case”. Zbl 1418.34097 Chartier, P.; Murua, A.; Sanz-Serna, J. M. 2 2017 Symplectic Runge-Kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. Zbl 1339.65243 Sanz-Serna, J. M. 31 2016 Computing normal forms and formal invariants of dynamical systems by means of word series. Zbl 1334.34087 Murua, A.; Sanz-Serna, J. M. 13 2016 A technique for studying strong and weak local errors of splitting stochastic integrators. Zbl 1353.65004 Alamo, A.; Sanz-Serna, J. M. 11 2016 Vibrational resonance: a study with high-order word-series averaging. Zbl 1432.34058 Murua, A.; Sanz-Serna, J. M. 8 2016 Adaptive multi-stage integrators for optimal energy conservation in molecular simulations. Zbl 1422.65447 Fernández-Pendás, Mario; Akhmatskaya, Elena; Sanz-Serna, J. M. 7 2016 Higher-order averaging, formal series and numerical integration. III: Error bounds. Zbl 1322.34057 Chartier, P.; Murua, A.; Sanz-Serna, J. M. 19 2015 Extra chance generalized hybrid Monte Carlo. Zbl 1352.65007 Campos, Cédric M.; Sanz-Serna, J. M. 9 2015 Numerical integrators for the hybrid Monte Carlo method. Zbl 1312.65209 Blanes, Sergio; Casas, Fernando; Sanz-Serna, J. M. 18 2014 Markov chain Monte Carlo and numerical differential equations. Zbl 1318.65007 Sanz-Serna, J. M. 14 2014 Optimal tuning of the hybrid Monte Carlo algorithm. Zbl 1287.60090 Beskos, Alexandros; Pillai, Natesh; Roberts, Gareth; Sanz-Serna, Jesus-Maria; Stuart, Andrew 66 2013 Higher-order averaging, formal series and numerical integration. II: The quasi-periodic case. Zbl 1257.34031 Chartier, P.; Murua, A.; Sanz-Serna, J. M. 17 2012 A formal series approach to averaging: exponentially small error estimates. Zbl 1246.34043 Chartier, Philippe; Murua, Ander; Sanz-Serna, Jesús María 16 2012 A multiscale technique for finding slow manifolds of stiff mechanical systems. Zbl 1332.65100 Ariel, G.; Sanz-Serna, J. M.; Tsai, R. 7 2012 A stroboscopic numerical method for highly oscillatory problems. Zbl 1246.65116 Paz Calvo, Mari; Chartier, Philippe; Murua, Ander; Sanz-Serna, Jesús María 5 2012 Riemann manifold Langevin and Hamiltonian Monte Carlo methods. With discussion and authors’ reply. Zbl 1411.62071 Girolami, Mark; Calderhead, Ben 248 2011 Hybrid Monte Carlo on Hilbert spaces. Zbl 1235.60091 Beskos, A.; Pinski, F. J.; Sanz-Serna, J. M.; Stuart, A. M. 45 2011 Numerical stroboscopic averaging for ODEs and DAEs. Zbl 1223.65063 Calvo, M. P.; Chartier, Ph.; Murua, A.; Sanz-Serna, J. M. 18 2011 Higher-order averaging, formal series and numerical integration. I: B-series. Zbl 1211.34052 Chartier, P.; Murua, A.; Sanz-Serna, J. M. 27 2010 Heterogeneous multiscale methods for mechanical systems with vibrations. Zbl 1241.65071 Calvo, M. P.; Sanz-Serna, J. M. 8 2010 Carrying an inverted pendulum on a bumpy road. Zbl 1209.34069 Calvo, Mari Paz; Sanz-Serna, Jesús María 1 2010 Modulated Fourier expansions and heterogeneous multiscale methods. Zbl 1167.65393 Sanz-Serna, J. M. 30 2009 Instabilities and inaccuracies in the integration of highly oscillatory problems. Zbl 1190.65186 Calvo, M. P.; Sanz-Serna, J. M. 4 2009 Mollified impulse methods for highly oscillatory differential equations. Zbl 1169.65081 Sanz-Serna, J. M. 20 2008 Stabilizing with a hammer. Zbl 1146.60313 Sanz-Serna, J. M. 1 2008 The numerical integration of relative equilibrium solutions. The nonlinear Schrödinger equation. Zbl 0954.65087 Durán, A.; Sanz-Serna, J. M. 45 2000 Long-time-step methods for oscillatory differential equations. Zbl 0927.65143 García-Archilla, B.; Sanz-Serna, J. M.; Skeel, R. D. 89 1999 Ergodicity of dissipative differential equations subject to random impulses. Zbl 0934.34047 Sanz-Serna, J. M.; Stuart, A. M. 25 1999 Order conditions for numerical integrators obtained by composing simpler integrators. Zbl 0946.65056 Murua, A.; Sanz-Serna, J. M. 21 1999 A shadowing result with applications to finite element approximation of reaction-diffusion equations. Zbl 0913.65079 Larsson, Stig; Sanz-Serna, J.-M. 8 1999 Error growth in the numerical integration of periodic orbits by multistep methods, with application to reversible systems. Zbl 0905.65082 Cano, B.; Sanz-Serna, J. M. 15 1998 The numerical integration of relative equilibrium solutions. Geometric theory. Zbl 0913.65069 Durán, A.; Sanz-Serna, J. M. 10 1998 Variable step implementation of geometric integrators. Zbl 0930.65136 Calvo, M. P.; López-Marcos, M. A.; Sanz-Serna, J. M. 8 1998 Long-time step methods for oscillatory differential equations. Zbl 0902.65026 García-Archilla, B.; Sanz-Serna, J. M.; Skeel, R. D. 2 1998 Accuracy and conservation properties in numerical integration: The case of the Korteweg-de Vries equation. Zbl 0876.65068 de Frutos, J.; Sanz-Serna, J. M. 33 1997 Error growth in the numerical integration of periodic orbits, with application to Hamiltonian and reversible systems. Zbl 0889.65081 Cano, B.; Sanz-Serna, J. M. 26 1997 Symplectic methods based on decompositions. Zbl 0889.65082 Araújo, A. L.; Murua, A.; Sanz-Serna, J. M. 23 1997 Geometric integration. Zbl 0886.65074 Sanz-Serna, J. M. 18 1997 Explicit symplectic integrators using Hessian-vector products. Zbl 0868.65056 López-Marcos, M. A.; Sanz-Serna, J. M.; Skeel, Robert D. 12 1997 Cheap enhancement of symplectic integrators. Zbl 0843.65050 López-Marcos, M. A.; Sanz-Serna, J. M.; Skeel, R. D. 12 1996 The number of conditions for a Runge-Kutta method to have effective order \(p\). Zbl 0867.65039 Butcher, J. C.; Sanz-Serna, J. M. 9 1996 Are Gauss-Legendre methods useful in molecular dynamics? Zbl 0856.65083 López-Marcos, M. A.; Sanz-Serna, J. M.; Díaz, J. C. 5 1996 Backward error analysis of symplectic integrators. Zbl 0871.65079 Sanz-Serna, J. M. 3 1996 A finite difference scheme for the \(K(2,2)\) compacton equation. Zbl 0840.65090 de Frutos, J.; López-Marcos, M. A.; Sanz-Serna, J. M. 24 1995 Lack of dissipativity is not symplecticness. Zbl 0844.65062 Portillo, A.; Sanz-Serna, J. M. 4 1995 Solving numerically Hamiltonian systems. Zbl 0862.70002 Sanz-Serna, J. M. 2 1995 Fourier techniques in numerical methods for evolutionary problems. Zbl 0826.65090 Sanz-Serna, J. M. 1 1995 Numerical Hamiltonian problems. Zbl 0816.65042 Sanz-Serna, J. M.; Calvo, M. P. 435 1994 An unconventional symplectic integrator of W. Kahan. Zbl 0815.65090 Sanz-Serna, J. M. 23 1994 Canonical \(B\)-series. Zbl 0791.65049 Calvo, M. P.; Sanz-Serna, J. M. 16 1994 Modified equations for ODEs. Zbl 0807.65074 Calvo, M. P.; Murua, A.; Sanz-Serna, J. M. 13 1994 The behavior of finite element solutions of semilinear parabolic problems near stationary points. Zbl 0811.65072 Larsson, S.; Sanz-Serna, J.-M. 12 1994 The non-existence of symplectic multi-derivative Runge-Kutta methods. Zbl 0816.65043 Hairer, E.; Murua, A.; Sanz-Serna, J. M. 9 1994 Erring and being conservative. Zbl 0801.65090 de Frutos, J.; Sanz-Serna, J. M. 2 1994 The development of variable-step symplectic integrators, with application to the two-body problem. Zbl 0785.65083 Calvo, M. P.; Sanz-Serna, J. M. 54 1993 High-order symplectic Runge-Kutta-Nyström methods. Zbl 0787.65056 Calvo, M. P.; Sanz-Serna, J. M. 34 1993 Partitioned Runge-Kutta methods for separable Hamiltonian problems. Zbl 0777.65042 Abia, L.; Sanz-Serna, J. M. 25 1993 Shadows, chaos, and saddles. Zbl 0784.65065 Sanz-Serna, J. M.; Larsson, S. 5 1993 Reasons for a failure. The integration of the two-body problem with a symplectic Runge-Kutta-Nyström code with stepchanging facilities. Zbl 0938.65534 Calvo, M. P.; Sanz-Serna, J. M. 1 1993 Symplectic integrators for Hamiltonian problems: An overview. Zbl 0762.65043 Sanz-Serna, J. M. 117 1992 An easily implementable fourth-order method for the time integration of wave problems. Zbl 0761.65074 de Frutos, J.; Sanz-Serna, J. M. 34 1992 Order conditions for canonical Runge-Kutta-Nyström methods. Zbl 0802.65089 Calvo, M. P.; Sanz-Serna, J. M. 18 1992 The numerical integration of Hamiltonian systems. Zbl 0766.65058 Sanz-Serna, J. M. 17 1992 Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods. Zbl 0735.65048 Eirola, T.; Sanz-Serna, J. M. 13 1992 A note on uniform in time error estimates for approximations to reaction- diffusion equations. Zbl 0781.65080 Sanz-Serna, J. M.; Stuart, A. M. 12 1992 The numerical study of blowup with application to a nonlinear Schrödinger equation. Zbl 0761.65099 Tourigny, Y.; Sanz-Serna, J. M. 10 1992 Variable steps for symplectic integrators. Zbl 0795.65049 Calvo, M. P.; Sanz-Serna, J. M. 10 1992 Symplectic Runge-Kutta and related methods: Recent results. Zbl 0779.58019 Sanz-Serna, J. M. 9 1992 Numerical ordinary differential equations vs. dynamical systems. Zbl 0764.34009 Sanz-Serna, J. M. 8 1992 Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods. Zbl 0741.65056 Eirola, T.; Sanz-Serna, J. M. 6 1992 On polynomials orthogonal with respect to certain Sobolev inner products. Zbl 0734.42016 Iserles, Arieh; Koch, P. E.; Nørsett, Syvert P.; Sanz-Serna, J. M. 112 1991 Order conditions for canonical Runge-Kutta schemes. Zbl 0785.65085 Sanz-Serna, J. M.; Abia, L. 48 1991 Pseudospectral method for the ”good” Boussinesq equation. Zbl 0735.65089 de Frutos, J.; Ortega, T.; Sanz-Serna, J. M. 31 1991 Two topics in nonlinear stability. Zbl 0746.65069 Sanz-Serna, J. M. 12 1991 A finite difference formula for the discretization of \(d^ 3/dx^ 3\) on nonuniform grids. Zbl 0727.65011 Garcia-Archilla, B.; Sanz-Serna, J. M. 11 1991 Numerical solution of a hyperbolic system of conservation laws with source term arising in a fluidized bed model. Zbl 0723.76077 Christie, I.; Ganser, G. H.; Sanz-Serna, J. M. 3 1991 A spectral method for a nonlinear equation arising in fluidized bed modelling. Zbl 0734.65081 Abia, L.; Sanz-Serna, J. M. 1 1991 A new class of results for the algebraic equations of implicit Runge- Kutta processes. Zbl 0738.65067 Sanz-Serna, J. M.; Griffiths, D. F. 1 1991 Nonlinear stability and convergence of finite-difference methods for the ”good” Boussinesq equation. Zbl 0749.65082 Ortega, T.; Sanz-Serna, J. M. 33 1990 Orthogonality and approximation in a Sobolev space. Zbl 0749.41030 Iserles, Arieh; Sanz-Serna, J. M.; Koch, P. E.; Nørsett, Syvert P. 21 1990 Equilibria of Runge-Kutta methods. Zbl 0693.65047 Hairer, E.; Iserles, A.; Sanz-Serna, J. M. 13 1990 A Hamiltonian, explicit algorithm with spectral accuracy for the ‘good’ Boussinesq system. Zbl 0728.76072 de Frutos, J.; Ortega, T.; Sanz-Serna, J. M. 12 1990 Remarks on methods for the computation of boundary-element integrals by co-ordinate transformation. Zbl 0693.65012 Sanz-Serna, J.; Doblare, M.; Alarcon, E. 11 1990 The spectral accuracy of a fully-discrete scheme for a nonlinear third order equation. Zbl 0721.65055 Abia, L.; Sanz-Serna, J. M. 5 1990 ...and 42 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,476 Authors 62 Sanz-Serna, Jesús María 38 Marcellán Español, Francisco 32 Wu, Xinyuan 27 Wang, Bin 26 Chartier, Philippe 24 Blanes, Sergio 24 Murua, Ander 23 Iserles, Arieh 21 Simos, Theodore E. 20 Casas, Fernando 19 Tang, Yifa 19 Wang, Yushun 17 Brugnano, Luigi 17 Xu, Da 15 Quispel, Gilles Reinout Willem 14 Butcher, John C. 14 Cano, Begoña 14 Duran, Angel 14 Verwer, Jan G. 14 Villatoro, Francisco R. 13 Dağ, İdris 13 Hairer, Ernst 13 Moreno-Balcázar, Juan José 13 Reich, Sebastian 12 Alonso-Mallo, Isaías 12 Calvo, M. P. 12 Franco, J. Méndez 12 López-Marcos, Juan Carlos 12 Lubich, Christian 12 McLachlan, Robert I. 12 Stuart, Andrew M. 11 Hong, Jialin 11 Iavernaro, Felice 11 Kalogiratou, Zacharoula 11 Sharapudinov, Idris Idrisovich 11 Tsitouras, Charalampos 10 Calvo, Manuel 10 Ferreira, José Augusto 10 Montijano, Juan Ignacio 10 Rández, Luis 10 Song, Songhe 9 Cai, Wenjun 9 Čiegis, Raimondas 9 Jackiewicz, Zdzislaw 9 Jiang, Chaolong 9 Liu, Changying 9 Liu, Kai 9 Méhats, Florian 9 Piñar, Miguel A. 9 Shi, Wei 9 Skeel, Robert D. 9 Sri Ranga, Alagacone 9 Sun, Yajuan 8 Abia, Luis María 8 Bao, Weizhu 8 Bou-Rabee, Nawaf M. 8 Cockburn, Bernardo 8 Dougalis, Vassilios A. 8 Frasca-Caccia, Gianluca 8 Jorge, Juan Carlos 8 Kulikov, Gennady Yur’evich 8 Leimkuhler, Benedict J. 8 Palencia, Cesar 8 Pérez, Teresa E. 8 Qian, Xu 8 Qin, Mengzhao 8 Rus, Francisco 8 Sandu, Adrian 8 Vilmart, Gilles 8 Wang, Jilu 8 Xiao, Aiguo 8 You, Xiong 7 Castillo, Paul E. 7 Celledoni, Elena 7 Ding, Xiaohua 7 Gómez, Sergio Alejandro 7 Ketcheson, David I. 7 Laburta, María Pilar 7 Lan, Shiwei 7 Leok, Melvin 7 Li, Buyang 7 López-marcos, Miguel Ángel 7 Martín de Diego, David 7 Meijer, Henk G. 7 Miyatake, Yuto 7 Ostermann, Alexander 7 Qiu, Wenlin 7 Saka, Bülent 7 Schratz, Katharina 7 Wang, Tingchun 7 Yang, Xuehua 7 Zanna, Antonella 7 Zhang, Haixiang 7 Zhu, Beibei 6 Angulo, Oscar 6 Cai, Yongyong 6 Condon, Marissa 6 Elenin, G. G. 6 Famelis, Ioannis Th. 6 Fejzullahu, Bujar Xh. ...and 2,376 more Authors all top 5 Cited in 312 Serials 164 Applied Numerical Mathematics 158 Journal of Computational and Applied Mathematics 148 Journal of Computational Physics 123 Applied Mathematics and Computation 65 Computers & Mathematics with Applications 50 Journal of Scientific Computing 48 BIT 46 Computer Methods in Applied Mechanics and Engineering 45 Numerische Mathematik 44 Mathematics of Computation 41 Numerical Algorithms 36 Computer Physics Communications 36 International Journal of Computer Mathematics 29 Journal of Mathematical Analysis and Applications 26 SIAM Journal on Numerical Analysis 26 Numerical Methods for Partial Differential Equations 25 Mathematics and Computers in Simulation 24 SIAM Journal on Scientific Computing 22 Physica D 21 Physics Letters. 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Mathematical Models & Methods in Applied Sciences 3 Journal of Statistical Computation and Simulation 3 Mathematical Problems in Engineering 3 Optimization Methods & Software ...and 212 more Serials all top 5 Cited in 50 Fields 1,616 Numerical analysis (65-XX) 719 Partial differential equations (35-XX) 374 Dynamical systems and ergodic theory (37-XX) 331 Ordinary differential equations (34-XX) 162 Fluid mechanics (76-XX) 161 Mechanics of particles and systems (70-XX) 111 Probability theory and stochastic processes (60-XX) 103 Harmonic analysis on Euclidean spaces (42-XX) 89 Special functions (33-XX) 80 Quantum theory (81-XX) 78 Statistics (62-XX) 70 Mechanics of deformable solids (74-XX) 61 Statistical mechanics, structure of matter (82-XX) 59 Integral equations (45-XX) 54 Biology and other natural sciences (92-XX) 40 Optics, electromagnetic theory (78-XX) 37 Calculus of variations and optimal control; optimization (49-XX) 30 Approximations and expansions (41-XX) 28 Difference and functional equations (39-XX) 28 Computer science (68-XX) 26 Systems theory; control (93-XX) 25 Real functions (26-XX) 24 Functional analysis (46-XX) 19 Operator theory (47-XX) 15 Classical thermodynamics, heat transfer (80-XX) 15 Operations research, mathematical programming (90-XX) 12 Differential geometry (53-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 9 Combinatorics (05-XX) 8 Associative rings and algebras (16-XX) 8 Geophysics (86-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Information and communication theory, circuits (94-XX) 5 Algebraic geometry (14-XX) 5 Topological groups, Lie groups (22-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 4 Integral transforms, operational calculus (44-XX) 4 Astronomy and astrophysics (85-XX) 2 Nonassociative rings and algebras (17-XX) 2 Functions of a complex variable (30-XX) 2 Relativity and gravitational theory (83-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Category theory; homological algebra (18-XX) 1 Measure and integration (28-XX) 1 Abstract harmonic analysis (43-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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