Symplectic Effective Order Numerical Methods for Separable Hamiltonian Systems

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Symplectic Numerical Integrators in Constrained Hamiltonian Systems

Recent work reported in the literature suggests that for the long-time integration of Hamiltonian dynamical systems one should use methods that preserve the symplectic (or canonical) structure of the ow. Here we investigate the symplecticness of numerical integrators for constrained dynamics, such as occur in molecular dynamics when bond lengths are made rigid in order to overcome stepsize limi...

متن کامل

Energy-conserving numerical methods for multi-symplectic Hamiltonian PDEs

In this paper, the discrete gradient methods are investigated for ODEs with first integral, and the recursive formula is presented for deriving the high-order numerical methods. We generalize the idea of discrete gradient methods to PDEs and construct the high-order energypreserving numerical methods for multi-symplectic Hamiltonian PDEs. By integrating nonlinear Schrödinger equation, some nume...

متن کامل

High-Order Symplectic Schemes for Stochastic Hamiltonian Systems

The construction of symplectic numerical schemes for stochastic Hamiltonian systems is studied. An approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desired order. In general the proposed symplectic schemes are fully implicit, and they become computationally expensive for mean square orders greater than two. However, for stochasti...

متن کامل

Second Order Conformal Symplectic Schemes for Damped Hamiltonian Systems

Numerical methods for solving weakly damped Hamiltonian systems are constructed using the popular Störmer-Verlet and implicit midpoint methods. Each method is shown to preserve dissipation of symplecticity and dissipation of angular momentum of an N -body system with pairwise distance dependent interactions. Necessary and sufficient conditions for second order accuracy are derived. Analysis for...

متن کامل

High order symplectic integrators for perturbed Hamiltonian systems

Abstract. We present a class of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form H = A + εB. We give a constructive proof that for all integer p, there exists an integrator with positive steps with a remainder of order O(τε + τ ε), where τ is the stepsize of the integrator. The analytical expressions of the leading terms of the remainders are given...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Symmetry

سال: 2019

ISSN: 2073-8994

DOI: 10.3390/sym11020142