Solution of Burgers' equation using the marker method

A new method for the solution of Burgers' equation is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, a rediscussed in some details. The marker method is applicable to a general class of nonlinear dispersive partial differential equations.