Analisis Galat Energi dan Galat Fase Metode Forward 4th Order Symplectic Chin-Chen untuk Kasus Sistem Osilator Harmonik Sederhana

Hasanuddin Hasanuddin

Abstract


Penelitian ini meninjau galat energi dan galat fase dari metode forward 4th order symplectic Chin-Chen (F4OS-CC) untuk kasus sistem osilator harmonik sederhana. Metode F4OS-CC merupakan suatu integrator yang bersifat symplectic dan time-reversible tanpa menggunakan selang waktu negatif. Simulasi osilasi harmonik sederhana dengan metode integrasi F4OS-CC dan metode Leapfrog menghasilkan galat energi terikat (tidak memiliki rambatan linier). Akan tetapi, metode F4OS-CC memiliki galat fase yang lebih besar jika dibandingkan dengan metode non-symplectic orde sama (metode Runge-Kutta orde 4). Galat fase dapat dikurangi dengan menggunakan selang waktu variabel yang bergantung terhadap posisi. Tetapi, rambatan galat energi menjadi meningkat secara linier.

Keywords


F4OS-CC, galat energi, galat fase, Runge-Kutta orde 4

Full Text:

PDF

References


Yoshida, H., Recent Progress in the Theory and Application of Symplectic Integrators, Celestial Mechanics and Dynamical Astronomy, 56pp.27–43, 1993.

Dehnen, W. and Read, J. ~I. I., N-body simulations of gravitational dynamics, European Physical Journal Plus, 126(5), pp.55, 2011.

Hut, P., Makino, J., and McMillan, S., Building a better leapfrog, Astrophysical Journal, 443pp.L93–L96, 1995.

Leimkuhler, B. and Reich, S. ,Simulating Hamiltonian Dynamics,Cambridge University Press, 2005.

Suzuki, M., General theory of fractal path integrals with applications to many-body theories and statistical physics, Journal of Mathematical Physics, 32(2), pp.400–407, 1991.

Dehnen, W. and Hernandez, D. ~M., Symplectic fourth-order maps for the collisional N-body problem, Monthly Notices of the Royal Astronomical Society, 465pp.1201–1217, 2017.

Chin, S. A. and Chen, C. R., Forward Symplectic Integrators for Solving Gravitational Few-Body Problems, Celestial Mechanics and Dynamical Astronomy, 91(3), pp.301–322, 2005.

Scuro, S. R. and Chin, S. A., Forward symplectic integrators and the long-time phase error in periodic motions, Phys. Rev. E, 71(5), pp.56703, 2005.

Chin, S. and Scuro, S. , Exact evolution of time-reversible symplectic integrators and their phase errors for the harmonic oscillator, Physics Letters A, 342(5–6), pp.397–403, 2005.




DOI: http://dx.doi.org/10.26418/positron.v10i2.40023

Refbacks

  • There are currently no refbacks.


Published by
Fakultas Matematika dan
Ilmu Pengetahuan Alam

                                                                               

In Cooperation with
Physical Society
of Indonesia

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.