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Symmetry 2019, 11(2), 142; https://doi.org/10.3390/sym11020142

Symplectic Effective Order Numerical Methods for Separable Hamiltonian Systems

1
Department of Mathematics, University of Engineering and Technology, Lahore 54890, Pakistan
2
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 45550, Pakistan
3
School of Natural Sciences, Department of Mathematics, National University of Sciences and Technology, Islamabad 44000, Pakistan
4
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]   |  

Abstract

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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