Solutions of regularized long wave equation with finite difference methods

This master thesis consists of five chapters. In the first chapter, some information is given about wave concept and wave equations. Also in this chapter, historical development of Regularized Long Wave (RLW) equation is mentioned. In the second chapter, some basic concepts are given about finite difference methods and von Neumann stability analysis. In the third chapter, RLW equation is firstly introduced and then its literature survey is presented. In addition, the problems which are the motion of a single solitary wave, the interaction of two solitary waves and the undular bore are introduced for RLW equation given with different initial and boundary conditions. The fourth chapter constitutes the main part of the thesis. In this chapter, the RLW equation is solved numerically as UUx nonlinear term in RLW equation is replaced by four different linear finite difference approximations and the stability analysis of the obtained each finite difference scheme is also investigated. The results obtained by applying model problems of each approximation are given in the tables and compared with the other results in the literature. Finally, in the fifth chapter, the results obtained by using four different linear finite difference approximations have been briefly evaluated.