nowadays, problems that naturally have a number of inherent geometrical properties are of great interest, and the numerical methods used to solve such problems must be chosen in such a way that the resulting solution preserve these properties. These types of schemes methods are called structure preserving methods. Splitting methods are one of the most widely used methods among geometric integrators, which are often used to overcome the complexity of computing problems, constructing accurate high order numerical algorithms and extension of the region of stability of methods. These ideas are used to overcome the computational complexity which is arisen in numerical solution of higher dimensional problems. In this thesis, a new splitting technique is implemented for solving parabolic and hyperbolic PDEs. As the main result, the new methods preserve the maximum principle unconditionally or with a mild condition on discretization parameters in comparison with well known methods. Damping of numerical solution in time evolution is investigated. For numerical solution of the Burgers’ equation, as a nonlinear problem, an iterative method based on the new splitting technique is presented.
