Symplectic exponential Runge–Kutta methods for solving nonlinear Hamiltonian systems

Mei, Lijie; Wu, Xinyuan

doi:10.1016/j.jcp.2017.03.018

Cited by 66 publications

(37 citation statements)

References 21 publications

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“…Thus the first statement is true. The second statement can be obtained immediately by considering Theorem 3.2 of [14]. Based on the above two results, the third one holds.…”

Section: Theorem 32mentioning

confidence: 65%

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Symmetric and symplectic exponential integrators for nonlinear Hamiltonian systems

Wang

2019

Applied Mathematics Letters

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This letter studies symmetric and symplectic exponential integrators when applied to numerically computing nonlinear Hamiltonian systems. We first establish the symmetry and symplecticity conditions of exponential integrators and then show that these conditions are extensions of the symmetry and symplecticity conditions of Runge-Kutta methods. Based on these conditions, some symmetric and symplectic exponential integrators up to order four are derived. Two numerical experiments are carried out and the results demonstrate the remarkable numerical behavior of the new exponential integrators in comparison with some symmetric and symplectic Runge-Kutta methods in the literature.

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“…Thus the first statement is true. The second statement can be obtained immediately by considering Theorem 3.2 of [14]. Based on the above two results, the third one holds.…”

Section: Theorem 32mentioning

confidence: 65%

“…Based on the above two results, the third one holds. The last result comes from Theorem 3.1 of [14].…”

Section: Theorem 32mentioning

confidence: 96%

Symmetric and symplectic exponential integrators for nonlinear Hamiltonian systems

Wang

2019

Applied Mathematics Letters

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“…Remark 2.2 It is noted that this kind of method belongs to exponential integrators, which have been widely developed and researched for solving highly oscillatory systems (see, e.g. [19,20,21,24,30,32]).…”

Section: Definition 21mentioning

confidence: 99%

Exponential energy-preserving methods for charged-particle dynamics in a strong and constant magnetic field

Wang

2021

Journal of Computational and Applied Mathematics

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In this paper, exponential energy-preserving methods are formulated and analysed for solving charged-particle dynamics in a strong and constant magnetic field. The resulting method can exactly preserve the energy of the dynamics. Moreover, it is shown that the magnetic moment of the considered system is nearly conserved over a long time along this exponential energy-preserving method, which is proved by using modulated Fourier expansions. Other properties of the method including symmetry and convergence are also studied. An illustrated numerical experiment is carried out to demonstrate the long-time behaviour of the method.

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“…With regard to this kind of exponential integrators, two useful properties are shown in [23] and we summarise them as follows. Theorem 2.3 (See [23]) If an RK method with the coefficients (5) is of order p, then the exponential integrator given by (4) is also of order p. Theorem 2.4 (See [23]) The exponential integrator defined by (4) is symplectic if the corresponding RK method (5) is symplectic.…”

Section: Exponential Integratorsmentioning

confidence: 99%

Volume-preserving exponential integrators and their applications

Wang

2019

Journal of Computational Physics

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Symplectic exponential Runge–Kutta methods for solving nonlinear Hamiltonian systems

Cited by 66 publications

References 21 publications

Symmetric and symplectic exponential integrators for nonlinear Hamiltonian systems

Symmetric and symplectic exponential integrators for nonlinear Hamiltonian systems

Exponential energy-preserving methods for charged-particle dynamics in a strong and constant magnetic field

Volume-preserving exponential integrators and their applications

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