An Approximation Procedure for Nonsymmetric, Nonlinear Hyperbolic Systems with Integral Boundary Conditions

Optimal order error estimates for two linearizations of a collocation process using tensor products of continuous, piecewise linear functions in space and time are derived for a class of nonsymmetric, nonlinear hyperbolic systems with integral boundary conditions. This procedure is a variant of the so-called box scheme. Error estimates are also derived for a generalization of these procedures to collocation based on continuous, piecewise polynomials of degree r in space tensored with continuous, piecewise linear functions in time.