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Symmetry 2019, 11(1), 11; https://doi.org/10.3390/sym11010011

A Complex Lie-Symmetry Approach to Calculate First Integrals and Their Numerical Preservation

1
School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad 44000, Pakistan
2
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
3
Department of BS and H, College of E and ME, National University of Sciences and Technology, Peshawar Road, Rawalpindi 46000, Pakistan
*
Author to whom correspondence should be addressed.
Received: 26 September 2018 / Revised: 24 October 2018 / Accepted: 31 October 2018 / Published: 24 December 2018
(This article belongs to the Special Issue Numerical Analysis or Numerical Method in Symmetry)
Full-Text   |   PDF [644 KB, uploaded 24 December 2018]   |  

Abstract

We calculated Noether-like operators and first integrals of a scalar second-order ordinary differential equation using the complex Lie-symmetry method. We numerically integrated the equations using a symplectic Runge–Kutta method. It was seen that these structure-preserving numerical methods provide qualitatively correct numerical results, and good preservation of first integrals is obtained. View Full-Text
Keywords: Hamiltonian system; complex Lagrangian; Noether symmetries; first integrals; symplectic Runge–Kutta methods Hamiltonian system; complex Lagrangian; Noether symmetries; first integrals; symplectic Runge–Kutta methods
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Irshad, W.; Habib, Y.; Farooq, M.U. A Complex Lie-Symmetry Approach to Calculate First Integrals and Their Numerical Preservation. Symmetry 2019, 11, 11.

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