B-spline finite element methods for numerical solution of the generalized Schrödinger equation

In this thesis, B-spline collocation method is proposed for numerical solutions of the generalized Schrödinger (GNLS) equation. In the first chapter, general information about the thesis is given and the purpose of the thesis is explained. In the next section, previous studies on the GNLS equation are examined. In the third chapter, The GNLS equation given with initial-boundary conditions, test problems including the propagation of solitary waves and the collision of two soliton waves, and time discretization with second and fourth order accuracy are explained. In the fourth, fifth, sixth, seventh, eighth and nineth chapters, the numerical solution of the GNLS equation is investigated. As the proposed method, time discretization with accuracy of two and four are primarily used. Then, while space discretization is performed for each time discretization, the collocation method by using B-spline functions with degrees five, six, seven, eight, nine and ten is proposed, respectively. At the end of each chapter, the accuracy of the proposed methods is examined using two test problems. In the tenth chapter, the obtained results are discussed. In the last section, some suggestions are given for future studies.