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Journal of Computational Physics, ISSN 0021-9991, 04/2017, Volume 335, pp. 846 - 864
Journal Article
Bulletin des sciences mathématiques, ISSN 0007-4497, 03/2019, Volume 151, pp. 51 - 65
We introduce a notion of p-rough integrator on any Banach manifolds which plays the role of weak geometric Hölder p-rough paths in the usual Banach space... 
Banach manifolds | Rough paths theory | Canonical form | MATHEMATICS, APPLIED | SPACES | Differential Geometry | Mathematics | Classical Analysis and ODEs
Journal Article
IMA Journal of Numerical Analysis, ISSN 0272-4979, 07/2012, Volume 32, Issue 3, pp. 1194 - 1216
We introduce a novel technique for constructing higher-order variational integrators for Hamiltonian systems of ordinary differential equations. In the... 
variational order | Hamiltonian ODEs | Lagrangian variational integrators | Euler-Lagrange equations | MATHEMATICS, APPLIED | MECHANICS | DISCRETE
Journal Article
Mathematical and Computer Modelling, ISSN 0895-7177, 2004, Volume 40, Issue 11, pp. 1225 - 1244
Journal Article
Computer Physics Communications, ISSN 0010-4655, 06/2019, Volume 239, pp. 33 - 52
Magnetic quadrupoles are essential components of particle accelerators like the Large Hadron Collider. In order to study numerically the stability of the... 
Symplectic methods | High order ODE methods | Particle accelerators | Hamilton equations | Magnetic fields | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MATHEMATICAL | Analysis
Journal Article
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 10/2012, Volume 22, Issue 10, pp. 1230033 - 1230033
Journal Article
ACM Transactions on Mathematical Software (TOMS), ISSN 0098-3500, 11/2012, Volume 39, Issue 1, pp. 1 - 28
Journal Article
Symmetry, ISSN 2073-8994, 02/2019, Volume 11, Issue 2, p. 246
The primary contribution of this work is to develop direct processes of explicit Runge-Kutta type (RKT) as solutions for any fourth-order ordinary differential... 
Runge-Kutta type methods | Order conditions | Quad-colored trees | B-series | Fourth-order ODEs | NUMERICAL-METHODS | LINEAR MULTISTEP METHOD | order conditions | MULTIDISCIPLINARY SCIENCES | quad-colored trees | fourth-order ODEs | ORDINARY DIFFERENTIAL-EQUATIONS | INITIAL-VALUE PROBLEMS
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2018, Volume 40, Issue 6, pp. B1517 - B1540
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 2010, Volume 199, Issue 9, pp. 700 - 711
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 2011, Volume 230, Issue 9, pp. 3413 - 3429
Journal Article
Mathematics and Computers in Simulation, ISSN 0378-4754, 02/2016, Volume 120, pp. 104 - 119
Zhang-gradient (ZG) method is a combination of Zhang dynamics (ZD) and gradient dynamics (GD) methods which are two powerful methods for online time-varying... 
Options | Zhang-gradient (ZG) controllers | Tracking control | Double-integrator system | MATLAB ODE solver | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SYNCHRONIZATION | MATHEMATICS, APPLIED | DESIGN | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NEURAL-NETWORKS | DYNAMICS
Journal Article
Annals of Functional Analysis, ISSN 2008-8752, 2014, Volume 5, Issue 1, pp. 77 - 93
In this paper several new inequalities of Gruss' type for Riemann-Stieltjes integral with monotonic nondecreasing integrators under various assumptions for... 
Functions of selfadjoint operators | Selfadjoint operators | Hölder continuous functions | Riemann-stieltjes integral | Functions of bounded variation | Grüss inequality | Gruss inequality | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDS | Riemann-Stieltjes integral | Holder continuous functions
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2011, Volume 33, Issue 2, pp. 488 - 511
Journal Article
Comptes rendus - Mécanique, ISSN 1631-0721, 10/2014, Volume 342, Issue 10-11, pp. 595 - 609
We change a previous time-stepping algorithm for solving a multi-scale Vlasov–Poisson system within a Particle-In-Cell method, in order to perform accurate... 
Paraxial approximation | Particle-In-Cell method | Exponential time differencing | Highly oscillatory ODEs | Long-time simulation | Vlasov–Poisson system | Vlasov-Poisson system | MECHANICS | Algorithms | Modeling and Simulation | Mathematics | Plasma Physics | Numerical Analysis | Physics | Computer Science
Journal Article
Communications in Computational Physics, ISSN 1815-2406, 07/2015, Volume 18, Issue 2, pp. 263 - 296
With the aim of solving in a four dimensional phase space a multi-scale Vlasov-Poisson system, we propose in a Particle-In-Cell framework a robust... 
highly oscillatory ODEs | Vlasov-Poisson system | Particle-In-Cell method | long-time simulation | Guiding-Center | SIMULATION | PHYSICS, MATHEMATICAL | EQUATION | SCHEMES | Modeling and Simulation | Analysis of PDEs | Numerical Analysis | Computer Science | Mathematics | Plasma Physics | Physics
Journal Article
SIAM JOURNAL ON SCIENTIFIC COMPUTING, ISSN 1064-8275, 2019, Volume 41, Issue 5, pp. A2911 - A2937
We present a methodology for constructing time integrators for solving systems of first-order ordinary differential equations by using interpolating... 
approximation theory | MATHEMATICS, APPLIED | parallelism | high-order | ODES | polynomial interpolation | time integration
Journal Article
Atmospheric Environment, ISSN 1352-2310, 2009, Volume 43, Issue 40, pp. 6287 - 6295
Air quality models compute the transformation of species in the atmosphere undergoing chemical and physical changes. The numerical algorithms used to predict... 
Operator splitting | Chemical integrator | Mass conservation | Chemical kinetics | Positive definiteness | CHEMISTRY PROBLEMS | SCHEME | ENVIRONMENTAL SCIENCES | SYSTEMS | METEOROLOGY & ATMOSPHERIC SCIENCES | EQUATION | STIFF ODE SOLVERS
Journal Article
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