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Abstrac. A collocation-Galerkin scheme is proposed for an initial-boundary value problem for a first order hyperbolic equation in one space dimension. The Galerkin equations satisfied by the approximating solution are obtained from a weak-weak formulation of the initial-boundary value problem. The collocation points are taken to be affine images of the roots of the Jacobian polynomials of degree r 1 on [0, 11 with respect to the weight function x(l x). Optimal L'(L2)-norm estimates of the error are derived.

A collocation-Galerkin method for a first order hyperbolic equation with space and time dependent coefficient