Journal of Current Researches on Engineering, Science and Technology (JoCREST)

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Abstract


Approximate Symmetries of Differential Equations

Symmetry methods, which have an important place for differential equations, were developed by Sophus Lie in the second half of the 19th century. Lie group theory provides a very systematic approach to the investigation of analytical solutions. Instead of solving the nonlinear equation directly, the system of linear equations determining symmetries is handled using this theory. Perturbation analysis, which can be applied to a wide range of classes, especially nonlinear equations, is another method. This method is based on the principle of obtaining approximate solutions by opening the dependent variables into an asymptotic series according to a small parameter. As a result of the combination of these two techniques, a new approach has been developed and three different approximate symmetry theories have been proposed through this method. In this study, first of all, these three approximate symmetry calculation methods are introduced and discussed one by one. After, applying them to a nonlinear equation, the approximate symmetries of this equation were calculated first. The exact symmetries of this equation were calculated then and finally, the functionality of these methods was compared.



Keywords
Approximate Symmetry, Perturbation, Nonlinear



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