Solutions of the Equal Width Wave (EW) equation with finite difference methods

This M.Sc. thesis consists of five chapters. In the first chapter, the aim of this study and its importance in the literature are explained. In the second chapter, some fundamental concepts as well as the classical finite difference methods which are going to be used in the thesis have been presented. In the third chapter, after some information about the Equal Width Wave (EW) equation has been given, the previous studies about the EW equation have been mentioned. Moreover, in this chapter, model problems considered for the EW equation have been presented. The fourth chapter contains the main part of the thesis. In this chapter, different linearizations have been used for the non-linear term UU_{x}. Then these linearizations have been applied to the model problems considered in the thesis. The obtained numerical results have been compared with analytical and numerical ones available in the literature, and the error norms L₂ and L_{∞} and the invariants have been given in the form of tables. Moreover, in this chapter, the stability analysis of the finite difference approximations used in the thesis has been investigated. In the fifth chapter, the obtained numerical results have been evaluated.