Diagonal implicit symplectic extended RKN methods for solving oscillatory Hamiltonian systems
Sign Up to like & getrecommendations! Published in 2019 at "Computational and Applied Mathematics"
DOI: 10.1007/s40314-019-0786-8
Abstract: This paper studies diagonal implicit symplectic extended Runge–Kutta–Nyström (ERKN) methods for solving the oscillatory Hamiltonian system $$H(q,p)=\dfrac{1}{2}p^\mathrm{T}p+\dfrac{1}{2}q^\mathrm{T}Mq+U(q)$$H(q,p)=12pTp+12qTMq+U(q). Based on symplecticity conditions and order conditions, we construct some diagonal implicit symplectic ERKN methods. The stability of… read more here.
Keywords: methods solving; implicit symplectic; diagonal implicit; solving oscillatory ... See more keywords
A dissipation-preserving scheme for damped oscillatory Hamiltonian systems based on splitting
Sign Up to like & getrecommendations! Published in 2021 at "Applied Numerical Mathematics"
DOI: 10.1016/j.apnum.2021.08.001
Abstract: Abstract In this paper, a new dissipation-preserving scheme is established for weakly dissipative perturbations of oscillatory Hamiltonian systems. The system exhibits a nonlinear oscillatory structure. The main oscillation is governed by a matrix M and… read more here.
Keywords: preserving scheme; scheme; hamiltonian systems; oscillatory hamiltonian ... See more keywords