Edit Profile Sanz-Serna, Jesús María Compute Distance To: Compute Author ID: sanz-serna.jesus-maria Published as: Sanz Serna, J. M.; Sanz Serna, Jesus; Sanz-Serna, Chus (J. M.); Sanz-Serna, J.; Sanz-Serna, J. M.; Sanz-Serna, J.-M.; Sanz-Serna, Jesus M.; Sanz-Serna, Jesus-Maria; Sanz-Serna, Jesús M.; Sanz-Serna, Jesús María Homepage: http://sanzserna.org/ External Links: MGP · Wikidata · ORCID · dblp Documents Indexed: 157 Publications since 1976, including 7 Books Reviewing Activity: 76 Reviews Biographic References: 1 Publication all top 5 Co-Authors 31 single-authored 15 Murua, Ander 14 Calvo, M. P. 9 Christie, Ian 9 Verwer, Jan G. 7 Abia, Luis M. 7 Chartier, Philippe 7 de Frutos, Javier 5 López-marcos, Miguel Ángel 4 Griffiths, David F. 4 Ortega, Tomás 4 Skeel, Robert D. 4 Stuart, Andrew M. 3 García-Archilla, Bosco 3 Iserles, Arieh 3 Larsson, Stig 3 McLeod, Robin J. Y. 3 Palencia, Cesar 3 Vadillo, Fernando 2 Akhmatskaya, Elena 2 Alamo, A. 2 Araujo, Anderson L. A. 2 Beskos, Alexandros 2 Blom, Joke G. 2 Bou-Rabee, Nawaf M. 2 Campos, Cédric Martínez 2 Cano, Begoña 2 Duran, Angel 2 Eirola, Timo 2 Fernández-Pendás, Mario 2 Ganser, Gary H. 2 Hairer, Ernst 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 Tourigny, Yves 2 Zhu, Beibei 2 Zygalakis, Konstantinos C. 1 Alarcón, Eva M. 1 Araújo, Aurélio L. 1 Ariel, Gil 1 Blanes, Sergio 1 Butcher, John C. 1 Casas, Fernando 1 Celledoni, Elena 1 Díaz, Juan Carlos 1 Doblaré, Manuel 1 Dopico, Froilán M. 1 Durán Martín, Angel 1 Fairweather, Graeme 1 Hundsdorfer, Willem H. 1 Kuo, Pen-yu 1 López Fernández-Asenjo, Félix Francisco 1 Mitchell, Andrew Ronald 1 Morris, John Ll. 1 Pillai, Natesh S. 1 Pinski, Frank J. 1 Portillo, A. M. 1 Radivojević, Tijana 1 Roberts, Gareth O. 1 Spijker, Marc N. 1 Tsai, Yen-Hsi Richard 1 Zanna Munthe-Kaas, Antonella all top 5 Serials 17 Journal of Computational Physics 14 IMA Journal of Numerical Analysis 10 Numerische Mathematik 10 SIAM Journal on Numerical Analysis 8 Applied Numerical Mathematics 7 Mathematics of Computation 7 SIAM Journal on Scientific Computing 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 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 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Discrete and Continuous Dynamical Systems. Series B 1 Stochastics and Dynamics 1 Communications on Pure and Applied Analysis 1 Multiscale Modeling & Simulation 1 Acta Numerica 1 BIT. Nordisk Tidskrift for Informationsbehandling 1 Applied Mathematics and Mathematical Computation 1 Applied Mathematics and Nonlinear Sciences all top 5 Fields 132 Numerical analysis (65-XX) 49 Ordinary differential equations (34-XX) 43 Partial differential equations (35-XX) 42 Dynamical systems and ergodic theory (37-XX) 28 Mechanics of particles and systems (70-XX) 10 Probability theory and stochastic processes (60-XX) 10 Quantum theory (81-XX) 5 Functional analysis (46-XX) 5 Fluid mechanics (76-XX) 3 History and biography (01-XX) 3 Associative rings and algebras (16-XX) 3 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 Approximations and expansions (41-XX) 2 Integral equations (45-XX) 2 Operator theory (47-XX) 2 Statistics (62-XX) 2 Mechanics of deformable solids (74-XX) 2 Operations research, mathematical programming (90-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 134 Publications have been cited 2,488 times in 1,611 Documents Cited by ▼ Year ▼ Numerical Hamiltonian problems. Zbl 0816.65042Sanz-Serna, J. M.; Calvo, M. P. 353 1994 Runge-Kutta schemes for Hamiltonian systems. Zbl 0655.70013Sanz-Serna, J. M. 124 1988 On polynomials orthogonal with respect to certain Sobolev inner products. Zbl 0734.42016Iserles, Arieh; Koch, P. E.; Nørsett, Syvert P.; Sanz-Serna, J. M. 97 1991 Symplectic integrators for Hamiltonian problems: An overview. Zbl 0762.65043Sanz-Serna, J. M. 93 1992 Long-time-step methods for oscillatory differential equations. Zbl 0927.65143García-Archilla, B.; Sanz-Serna, J. M.; Skeel, R. D. 72 1999 Product approximation for non-linear problems in the finite element method. Zbl 0469.65072Christie, I.; Griffiths, D. F.; Mitchell, A. R.; Sanz-Serna, J. M. 68 1981 A numerical method for a partial integro-differential equation. Zbl 0643.65098Sanz-Serna, J. M. 63 1988 Conservative and nonconservative schemes for the solution of the nonlinear Schrödinger equation. Zbl 0593.65087Sanz-Serna, J. M.; Verwer, J. G. 55 1986 Methods for the numerical solution of the nonlinear Schrödinger equation. Zbl 0555.65061Sanz-Serna, J. M. 54 1984 Convergence and order reduction of Runge-Kutta schemes applied to evolutionary problems in partial differential equations. Zbl 0589.65069Sanz-Serna, J. M.; Verwer, J. G.; Hundsdorfer, W. H. 52 1987 Petrov-Galerkin methods for nonlinear dispersive waves. Zbl 0451.65086Sanz-Serna, J. M.; Christie, I. 52 1981 The development of variable-step symplectic integrators, with application to the two-body problem. Zbl 0785.65083Calvo, M. P.; Sanz-Serna, J. M. 39 1993 Order conditions for canonical Runge-Kutta schemes. Zbl 0785.65085Sanz-Serna, J. M.; Abia, L. 39 1991 Optimal tuning of the hybrid Monte Carlo algorithm. Zbl 1287.60090Beskos, Alexandros; Pillai, Natesh; Roberts, Gareth; Sanz-Serna, Jesus-Maria; Stuart, Andrew 37 2013 On the scope of the method of modified equations. Zbl 0613.65079Griffiths, D. F.; Sanz-Serna, J. M. 36 1986 The numerical integration of relative equilibrium solutions. The nonlinear Schrödinger equation. Zbl 0954.65087Durán, A.; Sanz-Serna, J. M. 34 2000 Convergence of method of lines approximations to partial differential equations. Zbl 0546.65064Verwer, J. G.; Sanz-Serna, J. M. 32 1984 Soliton and antisoliton interactions in the “good” Boussinesq equation. Zbl 0673.35089Manoranjan, V. S.; Ortega, T.; Sanz-Serna, J. M. 30 1988 Stability and convergence in numerical analysis. III: Linear investigation of nonlinear stability. Zbl 0695.65042López-Marcos, J. C.; Sanz-Serna, J. M. 28 1988 An easily implementable fourth-order method for the time integration of wave problems. Zbl 0761.65074de Frutos, J.; Sanz-Serna, J. M. 26 1992 Pseudospectral method for the ”good” Boussinesq equation. Zbl 0735.65089de Frutos, J.; Ortega, T.; Sanz-Serna, J. M. 26 1991 High-order symplectic Runge-Kutta-Nyström methods. Zbl 0787.65056Calvo, M. P.; Sanz-Serna, J. M. 25 1993 Nonlinear stability and convergence of finite-difference methods for the ”good” Boussinesq equation. Zbl 0749.65082Ortega, T.; Sanz-Serna, J. M. 25 1990 Hybrid Monte Carlo on Hilbert spaces. Zbl 1235.60091Beskos, A.; Pinski, F. J.; Sanz-Serna, J. M.; Stuart, A. M. 24 2011 Higher-order averaging, formal series and numerical integration. I: B-series. Zbl 1211.34052Chartier, P.; Murua, A.; Sanz-Serna, J. M. 24 2010 Error growth in the numerical integration of periodic orbits, with application to Hamiltonian and reversible systems. Zbl 0889.65081Cano, B.; Sanz-Serna, J. M. 24 1997 A finite difference scheme for the \(K(2,2)\) compacton equation. Zbl 0840.65090de Frutos, J.; López-Marcos, M. A.; Sanz-Serna, J. M. 24 1995 Partitioned Runge-Kutta methods for separable Hamiltonian problems. Zbl 0777.65042Abia, L.; Sanz-Serna, J. M. 23 1993 An explicit finite-difference scheme with exact conservation properties. Zbl 0484.65062Sanz-Serna, J. M. 23 1982 Accuracy and conservation properties in numerical integration: The case of the Korteweg-de Vries equation. Zbl 0876.65068de Frutos, J.; Sanz-Serna, J. M. 22 1997 A method for the integration in time of certain partial differential equations. Zbl 0514.65085Sanz-Serna, J. M.; Manoranjan, V. S. 22 1983 Order conditions for numerical integrators obtained by composing simpler integrators. Zbl 0946.65056Murua, A.; Sanz-Serna, J. M. 21 1999 On simple moving grid methods for one-dimensional evolutionary partial differential equations. Zbl 0645.65060Blom, J. G.; Sanz-Serna, J. M.; Verwer, J. G. 20 1988 Symplectic Runge-Kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. Zbl 1339.65243Sanz-Serna, J. M. 19 2016 Symplectic methods based on decompositions. Zbl 0889.65082Araújo, A. L.; Murua, A.; Sanz-Serna, J. M. 19 1997 Split-step spectral schemes for nonlinear Dirac systems. Zbl 0675.65131de Frutos, J.; Sanz-Serna, J. M. 19 1989 A simple adaptive technique for nonlinear wave problems. Zbl 0653.65087Sanz-Serna, J. M.; Christie, I. 19 1986 Numerical stroboscopic averaging for ODEs and DAEs. Zbl 1223.65063Calvo, M. P.; Chartier, Ph.; Murua, A.; Sanz-Serna, J. M. 18 2011 Modulated Fourier expansions and heterogeneous multiscale methods. Zbl 1167.65393Sanz-Serna, J. M. 18 2009 Stability and convergence at the PDE/stiff ODE interface. Zbl 0671.65078Sanz-Serna, J. M.; Verwer, J. G. 18 1989 Geometric integration. Zbl 0886.65074Sanz-Serna, J. M. 17 1997 The numerical integration of Hamiltonian systems. Zbl 0766.65058Sanz-Serna, J. M. 17 1992 Orthogonality and approximation in a Sobolev space. Zbl 0749.41030Iserles, Arieh; Sanz-Serna, J. M.; Koch, P. E.; Nørsett, Syvert P. 17 1990 Ergodicity of dissipative differential equations subject to random impulses. Zbl 0934.34047Sanz-Serna, J. M.; Stuart, A. M. 16 1999 An unconventional symplectic integrator of W. Kahan. Zbl 0815.65090Sanz-Serna, J. M. 16 1994 A formal series approach to averaging: exponentially small error estimates. Zbl 1246.34043Chartier, Philippe; Murua, Ander; Sanz-Serna, Jesús María 15 2012 Canonical \(B\)-series. Zbl 0791.65049Calvo, M. P.; Sanz-Serna, J. M. 15 1994 Order conditions for canonical Runge-Kutta-Nyström methods. Zbl 0802.65089Calvo, M. P.; Sanz-Serna, J. M. 15 1992 Higher-order averaging, formal series and numerical integration. III: Error bounds. Zbl 1322.34057Chartier, P.; Murua, A.; Sanz-Serna, J. M. 14 2015 Higher-order averaging, formal series and numerical integration. II: The quasi-periodic case. Zbl 1257.34031Chartier, P.; Murua, A.; Sanz-Serna, J. M. 14 2012 Mollified impulse methods for highly oscillatory differential equations. Zbl 1169.65081Sanz-Serna, J. M. 14 2008 Error growth in the numerical integration of periodic orbits by multistep methods, with application to reversible systems. Zbl 0905.65082Cano, B.; Sanz-Serna, J. M. 14 1998 Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods. Zbl 0735.65048Eirola, T.; Sanz-Serna, J. M. 14 1992 Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods. Zbl 0741.65056Eirola, T.; Sanz-Serna, J. M. 14 1992 Modified equations for ODEs. Zbl 0807.65074Calvo, M. P.; Murua, A.; Sanz-Serna, J. M. 13 1994 Equilibria of Runge-Kutta methods. Zbl 0693.65047Hairer, E.; Iserles, A.; Sanz-Serna, J. M. 13 1990 An adaptive moving grid method for one-dimensional systems of partial differential equations. Zbl 0675.65098Verwer, J. G.; Blom, J. G.; Sanz-Serna, J. M. 13 1989 A general equivalence theorem in the theory of discretization methods. Zbl 0599.65034Sanz-Serna, J. M.; Palencia, C. 13 1985 The behavior of finite element solutions of semilinear parabolic problems near stationary points. Zbl 0811.65072Larsson, S.; Sanz-Serna, J.-M. 12 1994 A Hamiltonian, explicit algorithm with spectral accuracy for the ‘good’ Boussinesq system. Zbl 0728.76072de Frutos, J.; Ortega, T.; Sanz-Serna, J. M. 12 1990 Word series for dynamical systems and their numerical integrators. Zbl 1369.34022Murua, A.; Sanz-Serna, J. M. 11 2017 Explicit symplectic integrators using Hessian-vector products. Zbl 0868.65056López-Marcos, M. A.; Sanz-Serna, J. M.; Skeel, Robert D. 11 1997 Cheap enhancement of symplectic integrators. Zbl 0843.65050López-Marcos, M. A.; Sanz-Serna, J. M.; Skeel, R. D. 11 1996 Two topics in nonlinear stability. Zbl 0746.65069Sanz-Serna, J. M. 11 1991 Convergence analysis of one-step schemes in the method of lines. Zbl 0671.65077Sanz-Serna, J. M.; Verwer, J. G. 11 1989 Randomized Hamiltonian Monte Carlo. Zbl 1373.60129Bou-Rabee, Nawaf; Sanz-Serna, Jesús María 10 2017 Variable steps for symplectic integrators. Zbl 0795.65049Calvo, M. P.; Sanz-Serna, J. M. 10 1992 The numerical study of blowup with application to a nonlinear Schrödinger equation. Zbl 0761.65099Tourigny, Y.; Sanz-Serna, J. M. 10 1992 A finite difference formula for the discretization of \(d^ 3/dx^ 3\) on nonuniform grids. Zbl 0727.65011Garcia-Archilla, B.; Sanz-Serna, J. M. 10 1991 Remarks on methods for the computation of boundary-element integrals by co-ordinate transformation. Zbl 0693.65012Sanz-Serna, J.; Doblare, M.; Alarcon, E. 10 1990 A definition of stability for nonlinear problems. Zbl 0679.65039López-Marcos, J. C.; Sanz-Serna, J. M. 10 1988 Convergence of methods for the numerical solution of the Korteweg-de Vries equation. Zbl 0455.65082Kuo, Pen-Yu; Sanz-Serna, J. M. 10 1981 Markov chain Monte Carlo and numerical differential equations. Zbl 1318.65007Sanz-Serna, J. M. 9 2014 The non-existence of symplectic multi-derivative Runge-Kutta methods. Zbl 0816.65043Hairer, E.; Murua, A.; Sanz-Serna, J. M. 9 1994 A note on uniform in time error estimates for approximations to reaction- diffusion equations. Zbl 0781.65080Sanz-Serna, J. M.; Stuart, A. M. 9 1992 Equivalence theorems for incomplete spaces: An appraisal. Zbl 0559.65033Palencia, C.; Sanz-Serna, J. M. 9 1984 A Galerkin method for a nonlinear integro-differential wave system. Zbl 0525.73089Christie, I.; Sanz-Serna, J. M. 9 1984 Computing normal forms and formal invariants of dynamical systems by means of word series. Zbl 1334.34087Murua, A.; Sanz-Serna, J. M. 8 2016 Numerical ordinary differential equations vs. dynamical systems. Zbl 0764.34009Sanz-Serna, J. M. 8 1992 A study of the recursion \(y_{n+1}=y_ n+\tau y^ m_ n\). Zbl 0599.65086Sanz-Serna, J. M.; Verwer, J. G. 8 1986 Studies in numerical nonlinear instability. I. Why do leapfrog schemes go unstable? Zbl 0612.65052Sanz-Serna, J. M. 8 1985 Interpolation of the coefficients in nonlinear elliptic Galerkin procedures. Zbl 0542.65042Sanz-Serna, J. M.; Abia, L. 8 1984 An extension of the Lax-Richtmyer theory. Zbl 0523.65067Palencia, C.; Sanz-Serna, J. M. 8 1984 Numerical integrators for the hybrid Monte Carlo method. Zbl 1312.65209Blanes, Sergio; Casas, Fernando; Sanz-Serna, J. M. 7 2014 A shadowing result with applications to finite element approximation of reaction-diffusion equations. Zbl 0913.65079Larsson, Stig; Sanz-Serna, J.-M. 7 1999 Variable step implementation of geometric integrators. Zbl 0930.65136Calvo, M. P.; López-Marcos, M. A.; Sanz-Serna, J. M. 7 1998 The number of conditions for a Runge-Kutta method to have effective order \(p\). Zbl 0867.65039Butcher, J. C.; Sanz-Serna, J. M. 7 1996 Studies in numerical nonlinear instability. II. A new look at \(u_ t+uu_ x=0\). Zbl 0612.65053Vadillo, F.; Sanz-Serna, J. M. 7 1986 Extra chance generalized hybrid Monte Carlo. Zbl 1352.65007Campos, Cédric M.; Sanz-Serna, J. M. 6 2015 A multiscale technique for finding slow manifolds of stiff mechanical systems. Zbl 1332.65100Ariel, G.; Sanz-Serna, J. M.; Tsai, R. 6 2012 Long-time step methods for oscillatory differential equations. Zbl 0902.65026García-Archilla, B.; Sanz-Serna, J. M.; Skeel, R. D. 6 1998 Symplectic Runge-Kutta and related methods: Recent results. Zbl 0779.58019Sanz-Serna, J. M. 6 1992 Studies in numerical nonlinear instability. III. Augmented Hamiltonian systems. Zbl 0632.65129Sanz-Serna, J. M.; Vadillo, F. 6 1987 Nonlinear instability, the dynamic approach. Zbl 0651.65060Sanz-Serna, J. M.; Vadillo, F. 6 1986 Barrelledness conditions on \(c_0(E)\). Zbl 0396.46005Marquina, A.; Sanz Serna, J. M. 6 1979 Geometric integrators and the Hamiltonian Monte Carlo method. Zbl 1431.65004Bou-Rabee, Nawaf; Sanz-Serna, J. M. 5 2018 A technique for studying strong and weak local errors of splitting stochastic integrators. Zbl 1353.65004Alamo, A.; Sanz-Serna, J. M. 5 2016 A stroboscopic numerical method for highly oscillatory problems. Zbl 1246.65116Paz Calvo, Mari; Chartier, Philippe; Murua, Ander; Sanz-Serna, Jesús María 5 2012 Heterogeneous multiscale methods for mechanical systems with vibrations. Zbl 1241.65071Calvo, M. P.; Sanz-Serna, J. M. 5 2010 The numerical integration of relative equilibrium solutions. Geometric theory. Zbl 0913.65069Durán, A.; Sanz-Serna, J. M. 5 1998 Contractivity of Runge-Kutta methods for convex gradient systems. Zbl 1451.65092Sanz Serna, J. M.; Zygalakis, K. C. 1 2020 Geometric integrators and the Hamiltonian Monte Carlo method. Zbl 1431.65004Bou-Rabee, Nawaf; Sanz-Serna, J. M. 5 2018 Numerical Hamiltonian problems. Reprint of the 1994 original published by Chapman & Hall. Zbl 1418.65002Sanz-Serna, Jesús María; Calvo, M. P. 2 2018 Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods. Zbl 1416.65517Radivojević, Tijana; Fernández-Pendás, Mario; Sanz-Serna, Jesús María; Akhmatskaya, Elena 1 2018 Hopf algebra techniques to handle dynamical systems and numerical integrators. Zbl 1409.37082Murua, Ander; Sanz-Serna, Jesús M. 1 2018 Word series for dynamical systems and their numerical integrators. Zbl 1369.34022Murua, A.; Sanz-Serna, J. M. 11 2017 Randomized Hamiltonian Monte Carlo. Zbl 1373.60129Bou-Rabee, Nawaf; Sanz-Serna, Jesús María 10 2017 Palindromic 3-stage splitting integrators, a roadmap. Zbl 1378.65154Campos, Cédric M.; Sanz-Serna, J. M. 2 2017 Erratum to: “Higher-order averaging, formal series and numerical integration. II: The quasi-periodic case”. Zbl 1418.34097Chartier, P.; Murua, A.; Sanz-Serna, J. M. 1 2017 Symplectic Runge-Kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. Zbl 1339.65243Sanz-Serna, J. M. 19 2016 Computing normal forms and formal invariants of dynamical systems by means of word series. Zbl 1334.34087Murua, A.; Sanz-Serna, J. M. 8 2016 A technique for studying strong and weak local errors of splitting stochastic integrators. Zbl 1353.65004Alamo, A.; Sanz-Serna, J. M. 5 2016 Adaptive multi-stage integrators for optimal energy conservation in molecular simulations. Zbl 1422.65447Fernández-Pendás, Mario; Akhmatskaya, Elena; Sanz-Serna, J. M. 3 2016 Vibrational resonance: a study with high-order word-series averaging. Zbl 1432.34058Murua, A.; Sanz-Serna, J. M. 1 2016 Higher-order averaging, formal series and numerical integration. III: Error bounds. Zbl 1322.34057Chartier, P.; Murua, A.; Sanz-Serna, J. M. 14 2015 Extra chance generalized hybrid Monte Carlo. Zbl 1352.65007Campos, Cédric M.; Sanz-Serna, J. M. 6 2015 Markov chain Monte Carlo and numerical differential equations. Zbl 1318.65007Sanz-Serna, J. M. 9 2014 Numerical integrators for the hybrid Monte Carlo method. Zbl 1312.65209Blanes, Sergio; Casas, Fernando; Sanz-Serna, J. M. 7 2014 Optimal tuning of the hybrid Monte Carlo algorithm. Zbl 1287.60090Beskos, Alexandros; Pillai, Natesh; Roberts, Gareth; Sanz-Serna, Jesus-Maria; Stuart, Andrew 37 2013 A formal series approach to averaging: exponentially small error estimates. Zbl 1246.34043Chartier, Philippe; Murua, Ander; Sanz-Serna, Jesús María 15 2012 Higher-order averaging, formal series and numerical integration. II: The quasi-periodic case. Zbl 1257.34031Chartier, P.; Murua, A.; Sanz-Serna, J. M. 14 2012 A multiscale technique for finding slow manifolds of stiff mechanical systems. Zbl 1332.65100Ariel, G.; Sanz-Serna, J. M.; Tsai, R. 6 2012 A stroboscopic numerical method for highly oscillatory problems. Zbl 1246.65116Paz Calvo, Mari; Chartier, Philippe; Murua, Ander; Sanz-Serna, Jesús María 5 2012 Hybrid Monte Carlo on Hilbert spaces. Zbl 1235.60091Beskos, A.; Pinski, F. J.; Sanz-Serna, J. M.; Stuart, A. M. 24 2011 Numerical stroboscopic averaging for ODEs and DAEs. Zbl 1223.65063Calvo, M. P.; Chartier, Ph.; Murua, A.; Sanz-Serna, J. M. 18 2011 Higher-order averaging, formal series and numerical integration. I: B-series. Zbl 1211.34052Chartier, P.; Murua, A.; Sanz-Serna, J. M. 24 2010 Heterogeneous multiscale methods for mechanical systems with vibrations. Zbl 1241.65071Calvo, M. P.; Sanz-Serna, J. M. 5 2010 Carrying an inverted pendulum on a bumpy road. Zbl 1209.34069Calvo, Mari Paz; Sanz-Serna, Jesús María 1 2010 Modulated Fourier expansions and heterogeneous multiscale methods. Zbl 1167.65393Sanz-Serna, J. M. 18 2009 Instabilities and inaccuracies in the integration of highly oscillatory problems. Zbl 1190.65186Calvo, M. P.; Sanz-Serna, J. M. 3 2009 Mollified impulse methods for highly oscillatory differential equations. Zbl 1169.65081Sanz-Serna, J. M. 14 2008 Stabilizing with a hammer. Zbl 1146.60313Sanz-Serna, J. M. 1 2008 The numerical integration of relative equilibrium solutions. The nonlinear Schrödinger equation. Zbl 0954.65087Durán, A.; Sanz-Serna, J. M. 34 2000 Long-time-step methods for oscillatory differential equations. Zbl 0927.65143García-Archilla, B.; Sanz-Serna, J. M.; Skeel, R. D. 72 1999 Order conditions for numerical integrators obtained by composing simpler integrators. Zbl 0946.65056Murua, A.; Sanz-Serna, J. M. 21 1999 Ergodicity of dissipative differential equations subject to random impulses. Zbl 0934.34047Sanz-Serna, J. M.; Stuart, A. M. 16 1999 A shadowing result with applications to finite element approximation of reaction-diffusion equations. Zbl 0913.65079Larsson, Stig; Sanz-Serna, J.-M. 7 1999 Error growth in the numerical integration of periodic orbits by multistep methods, with application to reversible systems. Zbl 0905.65082Cano, B.; Sanz-Serna, J. M. 14 1998 Variable step implementation of geometric integrators. Zbl 0930.65136Calvo, M. P.; López-Marcos, M. A.; Sanz-Serna, J. M. 7 1998 Long-time step methods for oscillatory differential equations. Zbl 0902.65026García-Archilla, B.; Sanz-Serna, J. M.; Skeel, R. D. 6 1998 The numerical integration of relative equilibrium solutions. Geometric theory. Zbl 0913.65069Durán, A.; Sanz-Serna, J. M. 5 1998 Error growth in the numerical integration of periodic orbits, with application to Hamiltonian and reversible systems. Zbl 0889.65081Cano, B.; Sanz-Serna, J. M. 24 1997 Accuracy and conservation properties in numerical integration: The case of the Korteweg-de Vries equation. Zbl 0876.65068de Frutos, J.; Sanz-Serna, J. M. 22 1997 Symplectic methods based on decompositions. Zbl 0889.65082Araújo, A. L.; Murua, A.; Sanz-Serna, J. M. 19 1997 Geometric integration. Zbl 0886.65074Sanz-Serna, J. M. 17 1997 Explicit symplectic integrators using Hessian-vector products. Zbl 0868.65056López-Marcos, M. A.; Sanz-Serna, J. M.; Skeel, Robert D. 11 1997 Cheap enhancement of symplectic integrators. Zbl 0843.65050López-Marcos, M. A.; Sanz-Serna, J. M.; Skeel, R. D. 11 1996 The number of conditions for a Runge-Kutta method to have effective order \(p\). Zbl 0867.65039Butcher, J. C.; Sanz-Serna, J. M. 7 1996 Are Gauss-Legendre methods useful in molecular dynamics? Zbl 0856.65083López-Marcos, M. A.; Sanz-Serna, J. M.; Díaz, J. C. 5 1996 Backward error analysis of symplectic integrators. Zbl 0871.65079Sanz-Serna, J. M. 2 1996 A finite difference scheme for the \(K(2,2)\) compacton equation. Zbl 0840.65090de Frutos, J.; López-Marcos, M. A.; Sanz-Serna, J. M. 24 1995 Lack of dissipativity is not symplecticness. Zbl 0844.65062Portillo, A.; Sanz-Serna, J. M. 3 1995 Solving numerically Hamiltonian systems. Zbl 0862.70002Sanz-Serna, J. M. 1 1995 Fourier techniques in numerical methods for evolutionary problems. Zbl 0826.65090Sanz-Serna, J. M. 1 1995 Numerical Hamiltonian problems. Zbl 0816.65042Sanz-Serna, J. M.; Calvo, M. P. 353 1994 An unconventional symplectic integrator of W. Kahan. Zbl 0815.65090Sanz-Serna, J. M. 16 1994 Canonical \(B\)-series. Zbl 0791.65049Calvo, M. P.; Sanz-Serna, J. M. 15 1994 Modified equations for ODEs. Zbl 0807.65074Calvo, M. P.; Murua, A.; Sanz-Serna, J. M. 13 1994 The behavior of finite element solutions of semilinear parabolic problems near stationary points. Zbl 0811.65072Larsson, S.; Sanz-Serna, J.-M. 12 1994 The non-existence of symplectic multi-derivative Runge-Kutta methods. Zbl 0816.65043Hairer, E.; Murua, A.; Sanz-Serna, J. M. 9 1994 Erring and being conservative. Zbl 0801.65090de Frutos, J.; Sanz-Serna, J. M. 2 1994 The development of variable-step symplectic integrators, with application to the two-body problem. Zbl 0785.65083Calvo, M. P.; Sanz-Serna, J. M. 39 1993 High-order symplectic Runge-Kutta-Nyström methods. Zbl 0787.65056Calvo, M. P.; Sanz-Serna, J. M. 25 1993 Partitioned Runge-Kutta methods for separable Hamiltonian problems. Zbl 0777.65042Abia, L.; Sanz-Serna, J. M. 23 1993 Shadows, chaos, and saddles. Zbl 0784.65065Sanz-Serna, J. M.; Larsson, S. 4 1993 Reasons for a failure. The integration of the two-body problem with a symplectic Runge-Kutta-Nyström code with stepchanging facilities. Zbl 0938.65534Calvo, M. P.; Sanz-Serna, J. M. 1 1993 Symplectic integrators for Hamiltonian problems: An overview. Zbl 0762.65043Sanz-Serna, J. M. 93 1992 An easily implementable fourth-order method for the time integration of wave problems. Zbl 0761.65074de Frutos, J.; Sanz-Serna, J. M. 26 1992 The numerical integration of Hamiltonian systems. Zbl 0766.65058Sanz-Serna, J. M. 17 1992 Order conditions for canonical Runge-Kutta-Nyström methods. Zbl 0802.65089Calvo, M. P.; Sanz-Serna, J. M. 15 1992 Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods. Zbl 0735.65048Eirola, T.; Sanz-Serna, J. M. 14 1992 Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods. Zbl 0741.65056Eirola, T.; Sanz-Serna, J. M. 14 1992 Variable steps for symplectic integrators. Zbl 0795.65049Calvo, M. P.; Sanz-Serna, J. M. 10 1992 The numerical study of blowup with application to a nonlinear Schrödinger equation. Zbl 0761.65099Tourigny, Y.; Sanz-Serna, J. M. 10 1992 A note on uniform in time error estimates for approximations to reaction- diffusion equations. Zbl 0781.65080Sanz-Serna, J. M.; Stuart, A. M. 9 1992 Numerical ordinary differential equations vs. dynamical systems. Zbl 0764.34009Sanz-Serna, J. M. 8 1992 Symplectic Runge-Kutta and related methods: Recent results. Zbl 0779.58019Sanz-Serna, J. M. 6 1992 On polynomials orthogonal with respect to certain Sobolev inner products. Zbl 0734.42016Iserles, Arieh; Koch, P. E.; Nørsett, Syvert P.; Sanz-Serna, J. M. 97 1991 Order conditions for canonical Runge-Kutta schemes. Zbl 0785.65085Sanz-Serna, J. M.; Abia, L. 39 1991 Pseudospectral method for the ”good” Boussinesq equation. Zbl 0735.65089de Frutos, J.; Ortega, T.; Sanz-Serna, J. M. 26 1991 Two topics in nonlinear stability. Zbl 0746.65069Sanz-Serna, J. M. 11 1991 A finite difference formula for the discretization of \(d^ 3/dx^ 3\) on nonuniform grids. Zbl 0727.65011Garcia-Archilla, B.; Sanz-Serna, J. M. 10 1991 Numerical solution of a hyperbolic system of conservation laws with source term arising in a fluidized bed model. Zbl 0723.76077Christie, I.; Ganser, G. H.; Sanz-Serna, J. M. 3 1991 A spectral method for a nonlinear equation arising in fluidized bed modelling. Zbl 0734.65081Abia, L.; Sanz-Serna, J. M. 1 1991 A new class of results for the algebraic equations of implicit Runge- Kutta processes. Zbl 0738.65067Sanz-Serna, J. M.; Griffiths, D. F. 1 1991 Nonlinear stability and convergence of finite-difference methods for the ”good” Boussinesq equation. Zbl 0749.65082Ortega, T.; Sanz-Serna, J. M. 25 1990 Orthogonality and approximation in a Sobolev space. Zbl 0749.41030Iserles, Arieh; Sanz-Serna, J. M.; Koch, P. E.; Nørsett, Syvert P. 17 1990 Equilibria of Runge-Kutta methods. Zbl 0693.65047Hairer, E.; Iserles, A.; Sanz-Serna, J. M. 13 1990 A Hamiltonian, explicit algorithm with spectral accuracy for the ‘good’ Boussinesq system. Zbl 0728.76072de 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 0693.65012Sanz-Serna, J.; Doblare, M.; Alarcon, E. 10 1990 The spectral accuracy of a fully-discrete scheme for a nonlinear third order equation. Zbl 0721.65055Abia, L.; Sanz-Serna, J. M. 2 1990 Split-step spectral schemes for nonlinear Dirac systems. Zbl 0675.65131de Frutos, J.; Sanz-Serna, J. M. 19 1989 Stability and convergence at the PDE/stiff ODE interface. Zbl 0671.65078Sanz-Serna, J. M.; Verwer, J. G. 18 1989 An adaptive moving grid method for one-dimensional systems of partial differential equations. Zbl 0675.65098Verwer, J. G.; Blom, J. G.; Sanz-Serna, J. M. 13 1989 Convergence analysis of one-step schemes in the method of lines. Zbl 0671.65077Sanz-Serna, J. M.; Verwer, J. G. 11 1989 Stability of schemes for the numerical treatment of an equation modelling fluidized beds. Zbl 0674.76022Abia, L.; Christie, I.; Sanz-Serna, J. M. 1 1989 Runge-Kutta schemes for Hamiltonian systems. Zbl 0655.70013Sanz-Serna, J. M. 124 1988 A numerical method for a partial integro-differential equation. Zbl 0643.65098Sanz-Serna, J. M. 63 1988 Soliton and antisoliton interactions in the “good” Boussinesq equation. Zbl 0673.35089Manoranjan, V. S.; Ortega, T.; Sanz-Serna, J. M. 30 1988 Stability and convergence in numerical analysis. III: Linear investigation of nonlinear stability. Zbl 0695.65042López-Marcos, J. C.; Sanz-Serna, J. M. 28 1988 ...and 34 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,968 Authors 57 Sanz-Serna, Jesús María 36 Marcellán Español, Francisco 25 Wu, Xinyuan 23 Chartier, Philippe 21 Iserles, Arieh 21 Murua, Ander 19 Simos, Theodore E. 19 Wang, Bin 18 Tang, Yifa 16 Blanes, Sergio 15 Brugnano, Luigi 15 Verwer, Jan G. 14 Butcher, John C. 13 Cano, Begoña 13 Casas, Fernando 13 Dağ, İdris 13 Hairer, Ernst 13 Quispel, Gilles Reinout Willem 13 Reich, Sebastian 13 Villatoro, Francisco R. 12 Franco, J. Méndez 12 Moreno-Balcázar, Juan José 12 Wang, Yushun 12 Xu, Da 11 Duran, Angel 11 Kalogiratou, Zacharoula 11 López-Marcos, Juan Carlos 11 Sharapudinov, Idris Idrisovich 11 Stuart, Andrew M. 10 Alonso-Mallo, Isaías 10 Calvo, M. P. 10 Calvo, Manuel 10 Lubich, Christian 10 Montijano, Juan Ignacio 10 Rández, Luis 9 Ferreira, José Augusto 9 Iavernaro, Felice 9 Jorge, Juan Carlos 9 Méhats, Florian 9 Monovasilis, Theodoros 9 Piñar, Miguel A. 9 Skeel, Robert D. 8 Hong, Jialin 8 Leimkuhler, Benedict J. 8 Meijer, Henk G. 8 Palencia, Cesar 8 Pérez, Teresa E. 8 Qin, Mengzhao 8 Sun, Yajuan 8 Tsitouras, Charalampos 7 Abia, Luis M. 7 Celledoni, Elena 7 Jackiewicz, Zdzislaw 7 Kulikov, Gennady Yur’evich 7 Laburta, María Pilar 7 McLachlan, Robert I. 7 Rus, Francisco 7 Saka, Bülent 7 Sandu, Adrian 7 Vilmart, Gilles 7 Xiao, Aiguo 7 You, Xiong 6 Bao, Weizhu 6 Čiegis, Raimondas 6 Condon, Marissa 6 Elenin, G. G. 6 Fejzullahu, Bujar Xh. 6 Herbst, Ben M. 6 Hundsdorfer, Willem H. 6 Ismail, Mehmet S. 6 Lemou, Mohammed 6 López-marcos, Miguel Ángel 6 Miyatake, Yuto 6 Pinzón-Cortés, Natalia Camila 6 Portillo, A. M. 6 Ramos, Juan I. 6 Rodríguez García, José Manuel 6 Roeger, Lih-Ing Wu 6 Shi, Wei 6 Vázquez, Luis 6 Wang, Jilu 6 Zanna, Antonella 6 Zhang, Jingjing 6 Zhao, Xiaofei 5 Angulo, Oscar 5 Area, Iván 5 Bratsos, Athanassios G. 5 Campos, Cédric Martínez 5 Castillo, Paul E. 5 Chen, Jingbo 5 de Frutos, Javier 5 Dougalis, Vassilios A. 5 Famelis, Ioannis Th. 5 Godoy, Eduardo Paciência 5 Gómez, Sergio Alejandro 5 Habib, Yousaf 5 Higham, Desmond J. 5 Huang, Jingfang 5 Ibáñez González, Jacinto Javier 5 Ismail, Mohammad S. ...and 1,868 more Authors all top 5 Cited in 249 Serials 150 Journal of Computational and Applied Mathematics 148 Applied Numerical Mathematics 135 Journal of Computational Physics 112 Applied Mathematics and Computation 52 Computers & Mathematics with Applications 42 BIT 42 Numerische Mathematik 41 Computer Methods in Applied Mechanics and Engineering 40 Mathematics of Computation 35 Numerical Algorithms 34 Journal of Scientific Computing 29 Computer Physics Communications 26 Journal of Mathematical Analysis and Applications 26 International Journal of Computer Mathematics 19 Physics Letters. 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Zeitschrift für angewandte Mathematik und Physik 2 Journal of Functional Analysis 2 Kybernetes 2 Mathematische Annalen 2 Siberian Mathematical Journal 2 Systems & Control Letters 2 Journal of Complexity ...and 149 more Serials all top 5 Cited in 49 Fields 1,259 Numerical analysis (65-XX) 555 Partial differential equations (35-XX) 322 Dynamical systems and ergodic theory (37-XX) 300 Ordinary differential equations (34-XX) 135 Mechanics of particles and systems (70-XX) 128 Fluid mechanics (76-XX) 87 Harmonic analysis on Euclidean spaces (42-XX) 76 Special functions (33-XX) 63 Quantum theory (81-XX) 62 Probability theory and stochastic processes (60-XX) 50 Mechanics of deformable solids (74-XX) 44 Statistical mechanics, structure of matter (82-XX) 41 Biology and other natural sciences (92-XX) 38 Integral equations (45-XX) 32 Statistics (62-XX) 32 Optics, electromagnetic theory (78-XX) 26 Approximations and expansions (41-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 21 Difference and functional equations (39-XX) 21 Functional analysis (46-XX) 16 Real functions (26-XX) 16 Operator theory (47-XX) 15 Systems theory; control (93-XX) 14 Computer science (68-XX) 13 Classical thermodynamics, heat transfer (80-XX) 7 Combinatorics (05-XX) 7 Differential geometry (53-XX) 7 Operations research, mathematical programming (90-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Associative rings and algebras (16-XX) 5 Information and communication theory, circuits (94-XX) 4 History and biography (01-XX) 4 Topological groups, Lie groups (22-XX) 4 Geophysics (86-XX) 3 Integral transforms, operational calculus (44-XX) 3 Astronomy and astrophysics (85-XX) 2 General and overarching topics; collections (00-XX) 2 Algebraic geometry (14-XX) 2 Functions of a complex variable (30-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Measure and integration (28-XX) 1 Abstract harmonic analysis (43-XX) 1 Relativity and gravitational theory (83-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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