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

In this paper, numerical solution of Burgers–Fisher equation is presented based on the cubic B-spline quasi-interpolation. At first, the generalized Burgers–Fisher equation and the cubic B-spline quasi-interpolation are 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. Moreover, the stability of this method is studied. At last, the numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method. The main advantage of the resulting scheme is that the algorithm is very simple, so it is very easy to implement.