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2013•Unpublished venueRequires access

Symplectic Runge-Kutta Methods Generated by Trapezoidal Rule

Jiabo Tan

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Abstract

To preserve the symplecticity property, it is natural to require numerical integration of Hamiltonian systems to be symplectic. As a famous numerical integration, it is known that the trapezoidal rule is not symplectic. With the help of symplectic conditions of Runge-Kutta method and partitioned Runge-Kutta method, a symplectic partitioned Runge-Kutta method and a symplectic Runge-Kutta method are constructed on the basis of the trapezoidal rule in this paper.

About this research paper

What this paper is about

To preserve the symplecticity property, it is natural to require numerical integration of Hamiltonian systems to be symplectic. As a famous numerical integration, it is known that the trapezoidal rule is not symplectic. With the help of symplectic conditions of Runge-Kutta method and partitioned Runge-Kutta method, a symplectic partitioned Runge-Kutta method and a symplectic Runge-Kutta method are constructed on the basis of the trapezoidal rule in this paper.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

To preserve the symplecticity property, it is natural to require numerical integration of Hamiltonian systems to be symplectic. As a famous numerical integration, it is known that the trapezoidal rule is not symplectic. With the help of symplectic conditions of Runge-Kutta method and partitioned Runge-Kutta method, a symplectic partitioned Runge-Kutta method and a symplectic Runge-Kutta method are constructed on the basis of the trapezoidal rule in this paper.

Key concepts: Symplectic geometry, Runge–Kutta methods, Mathematics, Numerical integration, Symplectic integrator, Symplectic representation, Applied mathematics, Hamiltonian system

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