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Tang, Wensheng; Zhang, Jingjing

Symmetric integrators based on continuous-stage Runge-Kutta-Nyström methods for reversible systems. (English) Zbl 1429.65155

Appl. Math. Comput. 361, 1-12 (2019).
Summary: In this paper, we study symmetric integrators for solving second-order ordinary differential equations on the basis of the notion of continuous-stage Runge-Kutta-Nyström methods. The construction of such methods heavily relies on the Legendre expansion technique in conjunction with the symmetric conditions and simplifying assumptions for order conditions. New families of symmetric integrators as illustrative examples are presented. For comparing the numerical behaviors of the presented methods, some numerical experiments are also reported.

Cited in 4 Documents

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65P10 Numerical methods for Hamiltonian systems including symplectic integrators

Keywords:

continuous-stage Runge-Kutta-Nyström methods; reversible systems; symmetric integrators; simplifying assumptions; Legendre polynomials

Software:

LIMbook
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Full Text: DOI arXiv

References:

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