In this thesis, consistency and stability analysis of the traditional operator splitting methods are studied. We concentrate on how to improve the classical operator splitting methods via Zassenhaus product formula. In our approach, acceleration of the initial conditions and weighted polynomial ideas for each cases are individually handled and relevant algorithms are obtained. A new higher order operator splitting methods are proposed by the means of Zassenhaus product formula and rederive the consistency bound for traditional operator splitting methods. For unbounded operators, consistency analysis are proved by the C0-semigroup approach. We adapted the Von-Neumann stability analysis to operator splitting methods. General approach to use Von-Neumann stability analysis are discussed for the operator splitting methods. The proposed operator splitting methods and traditional operator splitting methods are applied to various ODE and PDE problems.