Numerical solutions of fractional order burgers equation by finite difference methods

In this thesis, which consists of five chapters, the first chapter is presented as an introduction. In this chapter, the historical and scientific development of the fractional analysis concept and the literature survey are given. In the second chapter, the basic concepts used in the study are examined in general terms. In the third chapter, the fractional order Burgers equation that are going to be used as a model problem in this study is introduced and a literature survey is given. Also, classical finite difference methods to be used in solving the equation are introduced in this chapter. In the fourth chapter, finite difference schemes are created for the fractional order Burgers equation. For the model problem, three different initial and boundary conditions are taken and implicit and Crank Nicolson finite difference schemes using inner iteration and Rubin Graves linearization techniques are utilized. A total of four different schemes were obtained for those methods. Numerical solutions were found with the help of these four schemes and the results were presented with the help of tables and figures. The fifth chapter was organized as conclusion and suggestions. A general evaluation of the results obtained in this chapter has also been made. Keywords: