Approximations for Burgers equations with C-N scheme and RBF collocation methods

The Burgers equation is one of the typical nonlinear evolutionary partial differential equations. In this paper, a mesh-free method is proposed to solve the Burgers equation using the finite difference and collocation methods. With the temporal discretization of the equation using C-N scheme, the solution is approximated spatially by Radial Basis Function (RBF). The numerical results of two different examples indicate the high accuracy and flexibility of the presented method.