Solving Nonlinear Ordinary Differential Equation of Electric Power Flow Model Using Lie Symmetry Method

@article{1703835,
      author = {Rhodah Machuma Mamuli, Dr Vincent N. Marani, Prof. Michael O. Oduor.},
      title = {Solving Nonlinear Ordinary Differential Equation of Electric Power Flow Model Using Lie Symmetry Method},
      journal = {Iconic Research And Engineering Journals},
      year = {2022},
      volume = {6},
      number = {4},
      pages = {23-27},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1703835.pdf},
      abstract = {A differential equation symmetry is a change that joins any solution to another solution of the structure. Lie groups and their infinitesimal generators can be naturally pro- longed to act on the space of independent variables. In this paper, we present analysis of Lie symmetry to solve a nonlinear ODE of an electric power flow model which is of form P(n,m,m^!,m^?,m^?! )=0. The search study uses Lie Symmetry analysis method to transform the equation by subjecting it to an extension generator and obtain determining equations, by reducing equations to lower order and find a general solution of the third or- der nonlinear heat conduction from the invariance related potential system under scaling. We exploited the use of prolongations (extended transformations), infinitesimal genera- tors, variation of symmetries, adjoint symmetries, invariant transformation problems and integrating factors.},
      keywords = {prolongations (extended transformations), infinitesimal generators, variation of symmetries, adjoint symmetries, invariant transformation problems and integrating factors.},
      month = {October},
  }