Numerical solutions of 1-dimensional burgers' equation by multiquadric radial basis function

This master thesis consists of three chapters. In the first chapter of the thesis, some information about 1-dimensional Burgers' equation, classical finite differences and radial basis functions which are going to be used in the next chapters are given. In the second chapter, which is constituting the main part of the thesis, a numerical scheme based on the classical finite difference formulation for time integration and the multiquadric radial basis function for space integration of the 1-dimensional Burgers' equation given by the initial and boundary conditions which are generally discussed has been obtained. In the last chapter of the thesis which is the third chapter, two test problems with analytical solution for Burgers' equation are considered. Numerical solutions of each test problem have been found using the scheme given in Chapter 2. The obtained solutions are presented in tables with analytical solution, some results available in the literature and error norms. In addition, some graphs have been given to demonstrate the continuity of the solutions obtained and the correct physical behavior of each problem.