Numerical solutions of nonlinear improved Boussinesq equation

This thesis constitutes five sections. In the first section, the basic terms, which were used in other sections, were described. Firstly; the definitions of both GBD, spline functions, B-spline functions, finite difference and finite elements, solitary waves. Then, Crank-Nicolson method was shortly described.In the second section, the numeric solution of GBD with compact finite difference scheme was made. For this solution firstly; compact finite difference algorithm was defined, the application of the method was made and thanks to the problems that was handled the advantageous parts of this method was determined.In the third section, the solution GBD, was made with Linear B-spline finite elements method. For this solution firstly; Linear B-spline Galerkin method was described, the application of the method was made, the validity of algorithm was proved thanks to the problems that was handled and with the help of this method; wave distinction, wave interaction and blow-up behavior was displayed.In the fourth section, the solution of GBD was made with quintik B-spline finite elements method. For this solution firstly; time decomposition was made, the method was applied and lastly, test problems that support numeric solutions was handled.In the fifth section, the numeric solution of GBD was made with finite difference method. For this solution, finite difference scheme was described, the application of the method was made and the effectiveness of the method was displayed thanks to the problems that was handled.