Application of least squares B-spline finite element method to differential problems

The main objective of this thesis is to obtain the numerical solutions of the RLW equation which has aquite importance in wave theory. For this objective, the least squares method is used. Some basic information about waves are given in the first chapter. RLW equation and its related test problems are introduced in the second chapter. Some introductory information about finite element method are presented in the third chapter. B-spline functions that are used as basis function are introduced in chapter four. Application of the numerical method for the RLW equation is constructed in the fifth chapter. In the application of the numerical method, firstly, the time discretization of the equation system is achieved by the help of Crank-Nicolson formulae. Then, the nonlinear terms in the equation are linearized. A uniform partition of the solution domain is considered for the space discretization. The Thomas algorithm is used for the solutions of the obtained matrix equations. von-Neumann analysis is employed for the stability of the method. The numerical method is tested on different test problems. Accuracy of the method is investigated by error norms and the conservative laws of RLW equation. Finally, a conclusion is given in the last chapter.