Error Estimates for Spectral and Pseudospectral Approximations of Hyperbolic Equations

The linear one-dimensional advection equation with variable coefficients and nonperiodic boundary conditions is considered. We investigate some spectral and pseudospectral (collocation) approximations of Jacobi and Legendre type (in the latter case the boundary condition is implicitly treated). Stability and convergence results in weighted norms are given; some precise estimates of the rate of convergence in terms of the regularity of the continuous solution are derived.