Sixth Parameter Symmetry for a Second Order Ordinary Differential Equation
Rodgers Adenyah *
Department of Mathematics and Computer Science, Pwani University, Kenya.
Barasa Joel
Department of Mathematics and Computer Science, Pwani University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Lie symmetry analysis is a powerful tool for solving ordinary differential equations whose results have been a huge driving force in the history of mathematics. Lie group theory is a very practical and handy mathematical approach and it can be used to obtain solutions to diverse problems in applied mathematics. Symmetry is an operation which leaves invariant that upon which it operates. A lie group or symmetry group is a group of transformations which maps any solution of the system to another solution of the same system. The symmetries of a given system of ordinary differential equations inform a lot about the closed form or the ability of the differential equation to solve. In this study, we use infinitesimal generators to obtain a sixth parameter symmetry for an ordinary differential equation. Symmetry properties and reduction of order differential equations yield solutions that are important in the field of science.
Keywords: Lie, symmetry, differential equations, infinitesimal generators, invariant