Applications of group preserving scheme for some differential equations with variable coefficients

This thesis is organized in …ve sections. In the …rst chapter, some general information about the group preserving scheme and its importance in the literature are given. In the second chapter, some fundamental concepts of the …nite di¤erence methods which are going to be used in the thesis have been presented. In the third chapter, Group preserving scheme has been investigated. The fourth and …fth chapters of this thesis constitude its original parts. In the fourth chapter, after general information about the linear Telegraf equation with variable and constant coe¢ cients have been given, the previous studies about the Telegraf equations have been mentioned. After that, Group preserving scheme is applied to these equations and the stability analysis of the approximation is given. Six model problems are solved by this method. The obtained results are compared with existing results in the literature, and they are given in the form of tables. In the …fth chapter, after general information about the Burgers equation has been given, Group preserving scheme is applied to this equation. Two model problems are solved by this method. The obtained numerical results are compared with existing results in the literature, and they are given in the form of tables.