Numerical solutions of equal width wawe equation by operator splitting trigonometric B-Spline collocation finite element method

This thesis consists of five chapters. In the introduction part of the thesis, some information has given about the relationship of partial differential equations with physical events in nature. In addition, in this section, a brief explanation has given about the equal-width wave equation and the operator splitting method, whose numerical solutions are obtained. In the second part of the thesis; Detailed information has given about the collocation method, finite element method, spline functions, B-spline functions, trigonometric cubic B-spline functions, and operator splitting methods. In the third part of the thesis, five model problems that the Equal Width Wave (EW) equation provides under certain initial and boundary conditions are introduced. In the fourth chapter of the thesis; Numerical solutions of the EW equation have obtained by operator splitting trigonometric B-spline collocation finite element method. Numerical solutions of the EW equation are obtained by both Lie-Trotter and Strang splitting methods. The conservation constants I_1, I_2 and I_3 provided by the EW equation are calculated by both methods and compared with each other. In addition, L_2 and L_∞ error norms, which are frequently used in the literature, are calculated with both Lie-Trotter and Strang splitting methods and compared with some studies in the literature. The graphs of the five model problems are drawn with the MATLAB 2015a program.