CONVERGENCE RESULTS FOR PSEUDOSPECTRAL APPROXIMATIONS OF HYPERBOLIC SYSTEMS BY A PENALTY-TYPE BOUNDARY TREATMENT

In a previous paper we have presented a new method of imposing boundary conditions in the pseudospectral Chebyshev approximation of a scalar hyperbolic equation. The novel idea of the new method is to collocate the equation at the boundary points as well as in the inner grid points, using the boundary conditions as penalty terms. In this paper we extend the above boundary treatment to the case of pseudospectral approximations to general constant-coefficient hyperbolic systems of equations, and we provide error estimates for the pseudospectral Legendre method. The same scheme can be implemented also in the general (even nonlinear) case.