Numerical solutions of equal width (EW) wave equation using trigonometric B-spline collocation finite element method

In the first chapter of this five-chapter study, after mentioning the main purpose of the thesis briefly, general information about the Equal Width Wave (EW) equation to be discussed in the thesis is given. In the second chapter, some important information about finite element methods and trigonometric B-spline base functions that will be used in the next sections are presented. In the third chapter of the thesis, some studies in the literature for the EW equation are mentioned. Also in this section, the model problems to be discussed for the EW equation in the thesis are explained together with the initial and boundary conditions. In the fourth chapter, five test problems are considered for the EW equation. Numerical schemes of each problem obtained by collocation finite element method based on trigonometric cubic base functions were solved. The numerical solutions obtained by the presented method were compared with the results of some other researchers available in the literature and also analytical results, if any. The obtained results, the error norms L₂ and L_{∞} and the conservation constants I₁, I₂ and I₃ are presented in tables. In addition, some graphs were given to demonstrate the continuity and correct physical behavior of the obtained numerical solutions for the problem. Also in this section, the stability analysis of the finite element approaches used in the thesis is examined. In the fifth chapter, which is the last chapter of the thesis, the numerical results obtained in the thesis are compared within themselves and those in the literature, and a brief discussion is presented