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Symmetry 2019, 11(2), 142;

Symplectic Effective Order Numerical Methods for Separable Hamiltonian Systems

Department of Mathematics, University of Engineering and Technology, Lahore 54890, Pakistan
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 45550, Pakistan
School of Natural Sciences, Department of Mathematics, National University of Sciences and Technology, Islamabad 44000, Pakistan
Business Administration Programme, Virtual University of Pakistan, Lahore 54000, Pakistan
Author to whom correspondence should be addressed.
Received: 7 January 2019 / Revised: 19 January 2019 / Accepted: 22 January 2019 / Published: 28 January 2019
(This article belongs to the Special Issue Numerical Analysis or Numerical Method in Symmetry)
Full-Text   |   PDF [357 KB, uploaded 28 January 2019]   |  


A family of explicit symplectic partitioned Runge-Kutta methods are derived with effective order 3 for the numerical integration of separable Hamiltonian systems. The proposed explicit methods are more efficient than existing symplectic implicit Runge-Kutta methods. A selection of numerical experiments on separable Hamiltonian system confirming the efficiency of the approach is also provided with good energy conservation. View Full-Text
Keywords: effective order; partitioned runge-kutta methods; symplecticity; hamiltonian systems effective order; partitioned runge-kutta methods; symplecticity; hamiltonian systems

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Ahmad, J.; Habib, Y.; Rehman, S.; Arif, A.; Shafiq, S.; Younas, M. Symplectic Effective Order Numerical Methods for Separable Hamiltonian Systems. Symmetry 2019, 11, 142.

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