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## References

SHOWING 1-10 OF 12 REFERENCES

HIGHER-ORDER GEOMETRIC INTEGRATORS FOR A CLASS OF HAMILTONIAN SYSTEMS

- Physics
- 2013

We discuss systematic extensions of the standard (Stormer–Verlet) method for integrating the differential equations of Hamiltonian mechanics. Our extensions preserve the symplectic geometry exactly,…

Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations

- Physics
- 2004

Numerical Hamiltonian Problems

- Computer Science, Mathematics
- 1994

Examples of Hamiltonian Systems, symplectic integration, and Numerical Methods: Checking preservation of area: Jacobians, and Necessity of the symplecticness conditions.

Systematic Improvement of Splitting Methods for the Hamilton Equations

- Physics
- 2012

We show how the standard (St{\"o}rmer-Verlet) splitting method for differential equations of Hamiltonian mechanics (with accuracy of order $\tau^2$ for a timestep of length $\tau$) can be improved in…

Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules

- Physics
- 1967

The equation of motion of a system of 864 particles interacting through a Lennard-Jones potential has been integrated for various values of the temperature and density, relative, generally, to a…

The NumPy Array: A Structure for Efficient Numerical Computation

- Computer ScienceComputing in Science & Engineering
- 2011

This effort shows, NumPy performance can be improved through three techniques: vectorizing calculations, avoiding copying data in memory, and minimizing operation counts.