Proceedings of the International Conference on COMPUTATION OF DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS

Feng, Kang; Shi, Zhong-Ci

doi:10.1142/9789812798176

Cited by 5 publications

(12 citation statements)

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“…The general methods of constructing volume-preserving methods include the generating function approach [14,15] and the splitting approach [16,17]. As the numerical methods based on generating functions are usually implicit, in the present study we choose to design volume-preserving numerical methods based on the splitting technique.…”

Section: Introductionmentioning

confidence: 99%

“…The integrators derived with the splitting technique can be high order and easy to compute. More importantly, when each component of the evolution vector fields belongs to the same Lie subalgebra L ⊂ V , where V is the Lie algebra defined by all the vector fields in the phase space with a Lie bracket, the resulting integrator is geometry-preserving if each subsystem is solved exactly or approximately by a corresponding geometric numerical method (see [16] for more details). This provides a very general and flexible approach of constructing geometric numerical integrators.…”

Section: Introductionmentioning

confidence: 99%

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Volume-preserving algorithms for charged particle dynamics

Yang

Sun

Liu

et al. 2015

Journal of Computational Physics

112

105

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Volume-preserving algorithms for charged particle dynamics

Yang

Sun

Liu

et al. 2015

Journal of Computational Physics

112

105

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“…Therefore, it is reasonable to pursue the numerical methods which preserve the phase-space volume. One practical tool to construct a VPA is the splitting technique, 20,21 which is applicable when the vector field Fðz; tÞ can be split into two or more incompressible sub-vector fields. 22 Because the subsystems are simpler, a VPA for each subsystem can usually be easily found.…”

mentioning

confidence: 99%

“…In fact, each sub-vector field belongs to a Lie subalgebra of the Lie algebra of the vector fields in the phase space. 20 If a volume-preserving integrator is found for each subsystem, according to the Lie group property, the corresponding VPA of the original system can be constructed from the sub-algorithms.…”

mentioning

confidence: 99%

Volume-preserving algorithm for secular relativistic dynamics of charged particles

et al. 2015

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Secular dynamics of relativistic charged particles has theoretical significance and a wide range of applications. However, conventional algorithms are not applicable to this problem due to the coherent accumulation of numerical errors. To overcome this difficulty, we develop a volumepreserving algorithm (VPA) with long-term accuracy and conservativeness via a systematic splitting method. Applied to the simulation of runaway electrons with a time-span over 10 magnitudes, the VPA generates accurate results and enables the discovery of new physics for secular runaway dynamics. V C 2015 AIP Publishing LLC. [http://dx.

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“…Since the appearance of symplectic algorithms, [2] structure-preserving algorithms for ordinary differential equations have attracted much attention. In Ref.…”

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confidence: 99%

Structure-Preserving Algorithms for the Lorenz System

Tie-Qiang¹,

Feng-Xiang²,

Chen³

2008

Chinese Phys. Lett.

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Based on a splitting method and a composition method, we construct some structure-preserving algorithms with first-order, second-order and fourth-order accuracy for a Lorenz system. By using the Liouville's formula, it is proven that the structure-preserving algorithms exactly preserve the volume of infinitesimal cube for the Lorenz system. Numerical experimental results illustrate that for the conservative Lorenz system, the qualitative behaviour of the trajectories described by the classical explicit fourth-order Runge-Kutta (RK4) method and the fifth-order Runge-Kutta-Fehlberg (RKF45) method is wrong, while the qualitative behaviour derived from the structure-preserving algorithms with different orders of accuracy is correct. Moreover, for the small dissipative Lorenz system, the norm errors of the structure-preserving algorithms in phase space are less than those of the Runge-Kutta methods.

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Proceedings of the International Conference on COMPUTATION OF DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS

Cited by 5 publications

References 0 publications

Volume-preserving algorithms for charged particle dynamics

Volume-preserving algorithms for charged particle dynamics

Volume-preserving algorithm for secular relativistic dynamics of charged particles

Structure-Preserving Algorithms for the Lorenz System

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