In this paper, we propose and analyze two kinds of novel and symmetric energy-preservmg formulae for the nonlinear oscillatory Hamiltonian system of second-order differential equations Aq＂ （t）＋ Bq（t） = f（q（t）...In this paper, we propose and analyze two kinds of novel and symmetric energy-preservmg formulae for the nonlinear oscillatory Hamiltonian system of second-order differential equations Aq＂ （t）＋ Bq（t） = f（q（t））, where A ∈ R^m×m is a symmetric positive definite matrix, B ∈ R^m×m is a symmetric positive semi-definite matrix that implicitly contains the main frequencies of the problem and f（q） = -VqV（q） for a real-valued function V（q）. The energy-preserving formulae can exactly preserve the Hamiltonian H（q＇,q） = 1/2q＇^TAq＇＋ 1/2q^TBq - V（q）. We analyze the properties of energy-preserving and convergence of the derived energy-preserving formula and obtain new efficient energy-preserving integrators for practical computation. Numerical experiments are carried out to show the efficiency of the new methods by the nonlinear Hamiltonian systems.展开更多
基金Supported by NSFC(Grant No.11571302)NSF of Shandong Province(Grant No.ZR2018MA024)the foundation of Scientific Project of Shandong Universities(Grant Nos.J17KA190 and KJ2018BAI031)
文摘In this paper, we propose and analyze two kinds of novel and symmetric energy-preservmg formulae for the nonlinear oscillatory Hamiltonian system of second-order differential equations Aq＂ （t）＋ Bq（t） = f（q（t））, where A ∈ R^m×m is a symmetric positive definite matrix, B ∈ R^m×m is a symmetric positive semi-definite matrix that implicitly contains the main frequencies of the problem and f（q） = -VqV（q） for a real-valued function V（q）. The energy-preserving formulae can exactly preserve the Hamiltonian H（q＇,q） = 1/2q＇^TAq＇＋ 1/2q^TBq - V（q）. We analyze the properties of energy-preserving and convergence of the derived energy-preserving formula and obtain new efficient energy-preserving integrators for practical computation. Numerical experiments are carried out to show the efficiency of the new methods by the nonlinear Hamiltonian systems.
