Numerical solutions of 1-dimensional Korteweg-de Vries (KdV) equation by Multiquadric Radial Basis Function

In the first chapter of this master thesis consisting of four chapters, the main purpose of the thesis is briefly explained.In the second chapter, some prominent information about Classical Finite Difference Methods, Radial Basis Function, the historical development of the KdV equation which are going to be used in the next chapters as well as solitary waves and solitons have been presented. In the third chapter which is constituting the main part of the thesis, a numerical scheme using appropriate finite difference formulation for time integration and the multiquadric radial basis function for space integration of the 1-dimensional KdV equation given by the initial and boundary conditions has been obtained. In the fourth chapter, three test problems are taken into consideration for KdV equation. Numerical solutions of each problem have been found by using the scheme given in the third chapter. The obtained solutions are compared with analytical solution and some results available in the literature. The obtained results together with the error norms L₂ and L∞ and the conservation constants have been given in tables. Additionally, some graphs have been given to show the continuity of the obtained numerical solutions and the fact that the correct physical behavior of the problem has been displayed.