Search Results - numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm

Algebraic dynamics algorithm: Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm

Authors: ShunJin Wang Hua Zhang

Source: Science in China Series G: Physics, Mechanics and Astronomy. 50:53-69

Access URL: https://link.springer.com/article/10.1007/s11433-007-2016-4
http://ui.adsabs.harvard.edu/abs/2007ScChG..50...53W/abstract
https://link.springer.com/content/pdf/10.1007/s11433-007-2016-4.pdf

Algebraic dynamics algorithm: Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm.

Authors: Wang, ShunJin Zhang, Hua

Source: Science in China. Series G: Physics & Astronomy; Feb2007, Vol. 50 Issue 1, p53-69, 17p

Numerical Integration of Lie--Poisson Systems While Preserving Coadjoint Orbits and Energy: Numerical integration of Lie-Poisson systems while preserving coadjoint orbits and energy

Authors: Kenth Engø Stig Faltinsen

Source: SIAM Journal on Numerical Analysis. 39:128-145

Subject Terms: Hamilton's equations, Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems, Geometric methods in ordinary differential equations, orbits, Numerical methods for Hamiltonian systems including symplectic integrators, 01 natural sciences, Casimirs, sin-Euler equations, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Fixed points and periodic points of dynamical systems, fixed-point index theory, local dynamics, Relations of dynamical systems with symplectic geometry and topology, Lie-Poisson systems, geometric integration, energy preserving algorithms, Newton iteration, 0101 mathematics, numerical experiments, rigid body

File Description: application/xml

Access URL: https://zbmath.org/1579025
https://doi.org/10.1137/s0036142999364212

Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations

Authors: Hairer, Ernst Lubich, Christian Wanner, Gerhard

Subject Terms: Geometric numerical integration, Differential equations on manifolds, Hamiltonian and reversible systems, Symplectic and symmetric methods, ddc:510

Access URL: https://archive-ouverte.unige.ch/unige:12343

Symplectic algebraic dynamics algorithm.

Authors: Wang, ShunJin Zhang, Hua

Source: Science in China. Series G: Physics & Astronomy; Apr2007, Vol. 50 Issue 2, p133-143, 11p

GniCodes — Matlab Programs for Geometric Numerical Integration

Authors: Hairer, Ernst Hairer, Martin

Source: Universitext ISBN: 9783540443193
Frontiers in Numerical Analysis pp. 199-240

Subject Terms: Geometric numerical integration, Reversible systems, Symmetric integrators, Runge-Kutta methods, Backward error analysis, Composition methods, Linear multistep methods, Matlab codes, ddc:510, Hamiltonian systems, Symplectic integrators

Access URL: https://archive-ouverte.unige.ch/unige:12569

Symplectic Geometric Algorithms for Hamiltonian Systems

Authors: Kang Feng Mengzhao Qin

Resource Type: eBook.

Subjects: Geometry, Differential, Algebraic topology, Mathematics—Data processing, Geometry, Quantum physics, Fluid mechanics

Categories: MATHEMATICS / Geometry / Differential, MATHEMATICS / Geometry / General, MATHEMATICS / Topology, SCIENCE / Physics / Quantum Theory, SCIENCE / Mechanics / Fluids, TECHNOLOGY & ENGINEERING / Mechanical, MATHEMATICS / Numerical Analysis

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations.

Authors: Wang, Shunjin Zhang, Hua

Source: Science in China. Series G: Physics & Astronomy; Dec2006, Vol. 49 Issue 6, p716-728, 13p

Forty years: Geometric numerical integration of dynamical systems in China.

Authors: Huang, Jianfei Liu, Na Tang, Yifa et al.

Source: International Journal of Modeling, Simulation & Scientific Computing; Oct2024, Vol. 15 Issue 5, p1-51, 51p

Subject Terms: HAMILTONIAN systems, DIFFERENTIAL geometry, NUMERICAL integration, PLASMA physics, DYNAMICAL systems

Positivity-preserving symplectic methods for the stochastic Lotka–Volterra predator-prey model.

Authors: Hong, Jialin Ji, Lihai Wang, Xu et al.

Source: BIT: Numerical Mathematics; Jun2022, Vol. 62 Issue 2, p493-520, 28p

Subject Terms: LOTKA-Volterra equations, HAMILTONIAN systems, RUNGE-Kutta formulas, STOCHASTIC systems, OPTIMISM

Comparison of two equivalent multisymplectic numerical methods for nonlinear wave equations.

Authors: Chen, Yao Duan, Hui Sun, Yajuan

Source: AIP Conference Proceedings; Sep2012, Vol. 1479 Issue 1, p1276-1279, 4p, 2 Graphs

Subject Terms: COMPARATIVE studies, NUMERICAL analysis, NONLINEAR wave equations, ERROR analysis in mathematics, MATHEMATICAL proofs, MATHEMATICAL variables

A Class of Meshless Structure-Preserving Algorithms for the Nonlinear Schrödinger Equation.

Authors: Wang, Jialing Zhou, Zhengting Lin, Zhoujin

Source: Computational Methods in Applied Mathematics; Oct2025, Vol. 25 Issue 4, p1003-1016, 14p

Subject Terms: NONLINEAR Schrodinger equation, MESHFREE methods, SYMPLECTIC spaces, NUMERICAL integration, NUMERICAL grid generation (Numerical analysis), COMPUTER simulation, INTERPOLATION algorithms, HAMILTONIAN systems

People: SCHROEDINGER, Erwin, 1887-1961

A new computationally efficient symplectic algorithm for forward modeling and attenuation-compensated reverse time migration Open Access.

Authors: Li, Jingshuang Zhang, Haixia Fang, Zhilong

Source: Journal of Geophysics & Engineering; Oct2025, Vol. 22 Issue 5, p1315-1332, 18p

Subject Terms: IMAGING systems in seismology, THEORY of wave motion, NUMERICAL analysis, COMPUTER simulation

A Geometric Numerical Integration with Simple Cell Mapping for Global Analysis of Nonlinear Dynamical Systems.

Authors: Huang, Fei-Long Chen, Li-Qun Jiang, Wen-An

Source: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering; Dec2024, Vol. 34 Issue 15, p1-20, 20p

Subject Terms: NUMERICAL integration, NONLINEAR systems, NONLINEAR analysis, ALGORITHMS

Practical perspectives on symplectic accelerated optimization.

Authors: Duruisseaux, Valentin Leok, Melvin

Source: Optimization Methods & Software; Dec2023, Vol. 38 Issue 6, p1230-1268, 39p

Subject Terms: OPTIMIZATION algorithms, NUMERICAL integration, GEOMETRIC approach, HAMILTONIAN systems, ALGORITHMS

High-order geometric integrators for the variational Gaussian approximation.

Authors: Moghaddasi Fereidani, Roya Vaníček, Jiří J. L.

Source: Journal of Chemical Physics; 9/7/2023, Vol. 159 Issue 9, p1-17, 17p

Subject Terms: TIME-dependent Schrodinger equations, ENERGY conservation, RUNGE-Kutta formulas

Research on Space Object Origin Tracing Approach Using Density Peak Clustering and Distance Feature Optimization.

Authors: Xue, Jinyan Zhang, Yasheng Tao, Xuefeng et al.

Source: Applied Sciences (2076-3417); Oct2025, Vol. 15 Issue 20, p10943, 12p

Subject Terms: CLUSTERING algorithms, MATHEMATICAL optimization, NEAR-Earth objects

A symplectic finite element method in time for periodic response of multibody systems.

Authors: Wang, Hao Wang, Chuanda Wang, Gang et al.

Source: Multibody System Dynamics; Dec2025, Vol. 65 Issue 4, p593-620, 28p

Semiexplicit K‐symplectic‐like methods with energy conservation for noncanonical Hamiltonian systems.

Authors: Zhu, Beibei Gu, Ran

Source: Numerical Methods for Partial Differential Equations; Nov2024, Vol. 40 Issue 6, p1-29, 29p

Subject Terms: HAMILTONIAN systems, ENERGY conservation, ALGORITHMS

A Novel Explicit Two-Derivative Runge-Kutta-Nyström Method with Energy Conservation for the Integration of Second-Order Periodic ODEs.

Authors: Sun, Zhuoyu Lee, K. C. Aziz, N. H. A. et al.

Source: European Journal of Pure & Applied Mathematics; Oct2025, Vol. 18 Issue 4, p1-45, 45p