Numerical solution of nonlinear Burgers' equation using high accuracy multi-quadric quasi-interpolation

In this paper, a numerical method is presented to approximate the solution to nonlinear Burgers' equation which is related to many scientific research topics. A numerical scheme by using high accuracy multi-quadric quasi-interpolation is presented in which a kind of multi-quadric quasi-interpolant is used to approximate the derivatives of the solution in spatial domain and finite difference is used to approximate the derivatives of the solution in temporal domain. The advantage of the scheme is that it is mesh free and in each time step only a multi-quadric quasi-interpolant is employed so that the algorithm is easy to implement. The numerical results of this scheme are also shown and compared with other numerical schemes.