Runge-Kutta methods for Hamiltonian systems in non-standard symplectic two-form

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Atıf İçin Kopyala

Karasozen B.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, cilt.66, ss.113-122, 1998 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 66
• Basım Tarihi: 1998
• Doi Numarası: 10.1080/00207169808804629
• Dergi Adı: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Sayfa Sayıları: ss.113-122
• Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

Runge-Kutta methods are applied to Hamiltonian systems on Poisson manifolds with a nonstandard symplectic two-form. It has been shown that the Gauss Legendre Runge-Kutta (GLRK) methods and combination of the partitioned Runge-Rutta methods of Lobatto IIIA and IIIb type are symplectic up to the second order in terms of the step size. Numerical results on Lotka-Volterra and Kermack-McKendrick epidemic disease model reveals that the application of the symplectic Runge-Kutta methods preserves the integral invariants of the underlying system for long-time computations.