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Solving Nonlinear Ordinary Differential Equation of Electric Power Flow Model Using Lie Symmetry Method
Subject area: Science,Engineering and Technology · Area of research: Masters
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.
References
[1] Ahmad Y., Al-Dweik, Mustafa M. T., Azad H. and Mahomed F. M. , Invariants of third order ordinary differential equation via point transfomation John Wiley and Sons Ltd,2015.
[2] Andrew A. O. Application of lie group analysis to Mathematical Model in epidemiology, 2015.
[3] Bluman G. W. and Cole J. D. Similarity Methods for Differential Equations; Springer-Verlag: New York, NY, USA, 1974.
[4] Elwakil, S. A., El-Labany, S. K., Zahran, M. A., & Sabry, R. (2002). Modified extended tanh-function method for solving nonlinear partial differential equations. Physics Letters A, 299(2-3), 179-188..
[5] George, O. , Aminer, T., and Ongati N.,Symmetry Analysis of Third Order Nonlinear Ordinary Differential Equation which is cubic in the Second Order Derivative, Vol. 10, 2016.
[6] Jiali Y. ,Fuzhi L. , and Lianbing S., Lie Symmetry Reductions and Exact Solutions of Multidimensional Double Dispersion Equation, Guangzhou University, china, 2017 uangzhou University, china, 2017.
[7] Oduor, M. E. O. Lie Symmetry Solutions Of The Generalized Burgers Equation, PhD thesis, Maseno University, Kenya, 2005.
How to cite this paper
@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},
}