NSTL国家科技图书文献中心

1. Discrete gradients in short-range molecular dynamics simulations NSTL国家科技图书文献中心

Grimm, Volker | Kliesch, Tobias ... - 《Numerical algorithms》 - 2024,96(3) - 1189～1220 - 共32页

摘要：Discrete gradients (DG) or more exactly discrete gradient methods are time integration schemes that are custom-built to preserve first integrals or Lyapunov functions of a given ordinary differential ...

关键词： Discrete gradient | Geometric numerical integration | Molecular dynamics | Linked cell method | Parallel computing | MOMENTUM CONSERVING METHODS | GEOMETRIC INTEGRATION | NUMERICAL INTEGRATORS | ARBITRARY ORDER | ENERGY...

2. USING AROMAS TO SEARCH FOR PRESERVED MEASURES AND INTEGRALS IN KAHAN'S METHOD NSTL国家科技图书文献中心

Bogfjellmo, Geir | Celledoni, Elena ... - 《Mathematics of computation》 - 2024,93(348) - 1633～1653 - 共21页

摘要：. The numerical method of Kahan applied to quadratic differential equations is known to often generate integrable maps in low dimensions and can in more general situations exhibit preserved measures a...

关键词： B-series methods | integrability | preservation of integrals and measures | Darboux polynomials | trees | aromatic trees | DISCRETIZATION

3. Birational maps from polarization and the preservation of measure and integrals NSTL国家科技图书文献中心

McLachlan, Robert, I | McLaren, David, I ... - 《Journal of physics, A. Mathematical and theoretical》 - 2023,56(36) - ARTN 365202～ - 共15页 - 被引量：1

摘要：The main result of this paper is the discretization of second-order Hamiltonian systems of the form x(sic) = K del W(x), where K is a constant symmetric matrix and W : R-n -> R is a polynomial of degr...

关键词： birational maps | Kahan mapping | geometric numerical integration | INTEGRABILITY | DISCRETIZATION

4. A novel 8-parameter integrable map in R-4 SCOPUS Scopus数据库 SCIE Web of Science核心 NSTL国家科技图书文献中心

Quispel, G. R. W. | McLaren, D., I ... - 《Journal of physics, A. Mathematical and theoretical》 - 2020,53(40) - 共6页 - 被引量：1

摘要：We present a novel 8-parameter integrable map in R-4. The map is measurepreserving and possesses two functionally independent 2-integrals, as well as a measure-preserving 2-symmetry.

关键词： discrete integrable systems | integrable map | polarisation

5. Generating a chain of maps which preserve the same integral as a given map SCOPUS Scopus数据库 EI 工程索引 SCIE Web of Science核心 NSTL国家科技图书文献中心

Tuwankotta, J. M. | van der Kamp, P. H.... - 《Physica Scripta: An International Journal for Experimental and Theoretical Physics》 - 2019,94(12) - 共11页

摘要：We generalise the concept of duality to systems of ordinary difference equations (or maps). We propose a procedure to construct a chain of systems of equations which are dual, with respect to an integ...

关键词： duality | mappings | lattice equations | integrals | complexity

6. Geometric and integrability properties of Kahan's method: the preservation of certain quadratic integrals NSTL国家科技图书文献中心

Celledoni, E. | McLaren, D., I ... - 《Journal of physics, A. Mathematical and theoretical》 - 2019,52(6) - 共9页 - 被引量：7

摘要：Given a quadratic vector field on R-n possessing a quadratic first integral depending on two of the independent variables, we give a constructive proof that Kahan's discretization method exactly prese...

关键词： integrability | discretization | ordinary differential equations

7. Three classes of quadratic vector fields for which the Kahan discretisation is the root of a generalised Manin transformation SCOPUS Scopus数据库 SCIE Web of Science核心 NSTL国家科技图书文献中心

van der Kamp, Peter ... | Celledoni, Elena ... - 《Journal of physics, A. Mathematical and theoretical》 - 2019,52(4) - 共10页 - 被引量：6

摘要：We apply Kahan's discretisation method to three classes of 2D quadratic vector fields with quadratic, resp. cubic, resp. quartic Hamiltonians. We show that the maps obtained in this way can be geometr...

关键词： Hamiltonian | Manin transformation | Kahan discretization | QRT mapping | quadratic vectorfield | Suslov problem | reduced Nahm equations

8. Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps NSTL国家科技图书文献中心

Celledoni, E. | Evripidou, C.... - 《Journal of physics, A. Mathematical and theoretical》 - 2019,52(31) - 共11页 - 被引量：6

摘要：In this letter we propose a systematic approach for detecting and calculating integrals and preserved measures of rational maps. The approach is based on the use of cofactors and discrete Darboux poly...

关键词： first integrals | Darboux polynomials | rational maps

9. Poisson structures for difference equations NSTL国家科技图书文献中心

Evripidou, C. A. | Quispel, G. R. W.... - 《Journal of physics, A. Mathematical and theoretical》 - 2018,51(47) - 共17页 - 被引量：2

摘要：We study the existence of log-canonical Poisson structures that are preserved by difference equations of a special form. We also study the inverse problem, given a log-canonical Poisson structure to f...

关键词： Poisson structures | difference equations | Hirota-Miwa equation

10. Some integrable maps and their Hirota bilinear forms NSTL国家科技图书文献中心

Hone, A. N. W. | Kouloukas, T. E.... - 《Journal of physics, A. Mathematical and theoretical》 - 2018,51(4) - 共30页 - 被引量：8

摘要：We introduce a two-parameter family of birational maps, which reduces to a family previously found by Demskoi, Tran, van der Kamp and Quispel (DTKQ) when one of the parameters is set to zero. The stud...