Numerical solution of Burgers' equation by cubic B-spline quasi-interpolation

In this paper, numerical solution of the Burgers' equation is presented based on the cubic B-spline quasi-interpolation. At. first the cubic B-spline quasi-interpolation is introduced. Moreover, the numerical scheme is presented, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable. The accuracy of the proposed method is demonstrated by some test problems. The numerical results are found in good agreement with exact solutions. The advantage of the resulting scheme is that the algorithm is very simple, so it is very easy to implement. (C) 2008 Elsevier Inc. All rights reserved.