More Recent Approximate Symmetry Theories

In the previous chapter, three approximate symmetry theorems appearing in the literature has already been discussed. In this chapter, three additional approximate symmetry theories will be discussed which was proposed by Pakdemirli (2024b) recently. Some sample ODEs having exact solutions are used for the task of comparing the performances of the new methods. The symmetries as well as solutions are compared with each other. It is shown that Lie algebras may be extended, symmetries of the approximate methods may be retrieved from the exact symmetries or symmetries may be only a subgroup of the exact symmetries depending on the specific method and equation considered. With the aid of approximate symmetries, both approximate solutions and exact solutions can be retrieved.