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Integrability of systems of ordinary differential equations via Lie point symmetries
  • Fatma Al-Kindi,
  • Fazal Mahomed,
  • Muhammad Ziad
Fatma Al-Kindi
Sultan Qaboos University College of Science
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Fazal Mahomed
Wits University
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Muhammad Ziad
Sultan Qaboos University College of Science
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Peer review status:UNDER REVIEW

02 Apr 2020Submitted to Mathematical Methods in the Applied Sciences
03 Apr 2020Assigned to Editor
03 Apr 2020Submission Checks Completed
08 Apr 2020Reviewer(s) Assigned

Abstract

The existing literature discusses different strategies to solve a scalar ordinary differential equation using Lie point symmetries. We focus on three of these strategies in order to frame methods for finding solutions of non-linear systems of ordinary differential equations. These include Lie's integration theorem, method of successive reduction of order and the method of using the invariants of the admitted symmetry generators. Illustrative examples and those taken from mechanics are presented to highlight the use of these methods.