Splitting Methods with Modified Potentials and Application to the Damped Wave Equation

In this report we study and compare particular integration methods to solve ordinary differential equations, which are separable in solvable parts. The main source for this work is the article of Blanes and Casas: "On the necessity of negative coefficient for operator splitting schemes of order higher than two", which was published by ELSEVIER in 2004. After a brief introduction and some preliminaries on fundamental aknownledged, namely the flow of a differential equation which will allow to construct splitting schemes, we start the third part of this work with some definitions and fundamental theorems for general splitting schemes. At the end of this section, we will look more carefully on some special schemes, with modified potentials. In the fourth part, we study and compare some of the different methods seen in the third part of this report on an ordinary separable differential equation. In fifth part, we use these splitting schemes on the damped wave equation and look at the conservation of the Energy. Finally, you will find the main MATLAB code in the annexe.