In this thesis, convergency and stability analysis are studied for the non-autonomous differential equations. Not only classical operator splitting methods; Lie Trother splitting, symmetrically weighted splitting and Strang splitting but also iterative splitting method which is recent popular technique of operator splitting methods are considered. We concentrate on how to improve the operator splitting methods with the help of the Magnus expansion. In addition, we construct a new symmetric iterative splitting scheme. Then, we also study its convergence properties by using the concepts of stability, consistency and order. For this purpose, we use C0 semigroup techniques. Finally, several numerical examples are illustrated in order to confirm our theoretical results by comparing the new symmetric iterative splitting method with frequently used operator splitting methods.