On the numerical solution of the 1-dimensional Rosenau equation

In the first chapter of this master's thesis, which consists of six chapters, the purpose of the thesis is mentioned after giving brief information about the history of the Rosenau equation considered in the thesis. In the second chapter, the conservative finite difference approach used in the thesis is introduced, and after giving information about the Rosenau equation, the model problems considered in the thesis study are introduced. In the third chapter, the conservative finite difference approach is applied in the Rosenau equation, instead of the non-linear term, 3different linearization techniques are used and the obtained numerical schemes are applied to the model problems introduced in the previous chapter. The numerical results obtained by applying the schemes are given in tables and graphics. Since the stability analyzes of the obtained numerical schemes will be similar, stability analysis of the scheme obtained only with LIN-1 is examined by the von Neumann method. In the fourth chapter, the Rosenau equation was split by time and instead of the non-linear term, the linearization techniques given in Chapter 3 are used to obtain numerical schemes with conservative finite difference approach. Numerical results are calculated by applying the obtained numerical schemes to the model problems given in Chapter 2. Numerical results are given in tables and graphs. The stability analysis of the numerical schemes obtained only with LİN-1 is analyzed by the von Neumann method. In the fifth chapter, numerical schemes are obtained by applying linearization techniques and conservative finite difference approach given in the previous chapters to the Rosenau equation split by position obtained by applying the u_{xx}=v transformation. Numerical results were found by applying the obtained numerical schemes to the model problems given in Chapter 2. The numerical results are presented in tables and graphs. In this section, the stability analysis of the scheme obtained by LİN-1 is analyzed using the von Neumann method. Finally, the results obtained from all methods and linearization techniques applied in the sixth chapter are compared within themselves in graphs for each model problem, and prominent methods and linearizations are presented.