A numerical solution of the Burgers' equation using cubic B-splines

In the present paper numerical solutions of the one-dimensional Burgers' equation are obtained by a method based on collocation of cubic B-splines over finite elements. The accuracy of the proposed method is demonstrated by three test problems. The numerical results are found in good agreement with exact solutions. Time-space integration of the Burgers' equation yields a system of difference equation which is shown to be unconditionally stable.