Numerical solutions of the Burgers' equation with İtrang İplitting method based on Crank-Nicolson finite diferance scheme

In this thesis, the numerical solutions of the 1-dimensional Burgers' equation obtained by Strang splitting method based on Crank-Nicolson finite difference scheme have been analyzed in four chapter. In the first chapter, a summary of the literature about 1-dimensional Burgers' equation has been given. In the second chapter, finite difference methods and Taylor series expansion are examined. Using the Taylor series expansion, the finite difference formulations are presented. Crank-Nicolson finite difference approach of the Burgers equation has been given. The analytical solution of the 1-dimensional Burgers' equation for two model problems has been obtained by using Hopf-Cole transformation. In the third chapter, the Lie-Trotter and Strang splitting methods have been explained and their local errors have been presented. Differen lineerization technique has been presented for finite difference methods. In the fourth chapter, the numerical solutions of the model problems have been obtained by using Strang splitting method based on the Crank-Nicolson finite difference method and different lineerization technique. The numerical solutions have been compared with analytical solutions.