Traveling-wave solutions for a discrete Burgers equation with nonlinear diffusion Original Research Article

We construct a nonstandard finite difference (NSFD) scheme for a Burgers type partial differential equation (PDE) for which the diffusion coefficient has a linear dependence on the dependent variable. After a study of this PDEʹs traveling-wave solutions, we examine the corresponding properties of the NSFD construction. Our work demonstrates the dynamic consistency of the discretization.