On the approximation of the transport equation by the method of weighted residuals

A general class of approximate models for the transport equation is derived by the Weighted Residual Method using polynomial trial and test spaces. For two, particularly relevant, of such models a closed form of the approximate solution is given in the Laplace-transform domain. A strict connection is established between the approximate transfer function and the Padé approximants to exp(-sx). Furthermore it is shown that Galerkin model minimizes in the considered class a measure of the initial state approximation error. Finally an application to the solution of systems of first order hyperbolic equations is reported.