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Efficient Energy-preserving Methods for General Nonlinear Oscillatory Hamiltonian System.
- Source :
-
Acta Mathematica Sinica . Dec2018, Vol. 34 Issue 12, p1863-1878. 16p. - Publication Year :
- 2018
-
Abstract
- In this paper, we propose and analyze two kinds of novel and symmetric energy-preserving formulae for the nonlinear oscillatory Hamiltonian system of second-order differential equations Aq″ (t)+ Bq(t) = f(q(t)), where A ∈ ℝm×m is a symmetric positive definite matrix, B ∈ ℝm×m is a symmetric positive semi-definite matrix that implicitly contains the main frequencies of the problem and f(q) = −∇qV (q) for a real-valued function V (q). The energy-preserving formulae can exactly preserve the Hamiltonian H(q′,q)=12q′TAq′+12qTBq+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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 34
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 133200413
- Full Text :
- https://doi.org/10.1007/s10114-018-6300-1