Pii: S0168-9274(02)00109-5

In this paper we give error estimates on the random projection methods, recently introduced by the authors, for numerical simulations of the hyperbolic conservation laws with stiff reaction terms: ut + f (u)x =− ε (u− α)(u2 − 1), −1 < α < 1. In this problem, the reaction time ε is small, making the problem numerically stiff. A classic spurious numerical phenomenon—the incorrect shock speed—occurs when the reaction time scale is not properly resolved numerically. The random projection method, a fractional step method that solves the homogeneous convection by any shock capturing method, followed by a random projection for the reaction term, was introduced in [J. Comput. Phys. 163 (2000) 216–248] to handle this numerical difficulty. In this paper, we prove that the random projection methods capture the correct shock speed with a first order accuracy, if a monotonicity-preserving method is used in the convection step. We also extend the random projection method for more general source term − 1 ε g(u), which has finitely many simple zeroes and satisfying ug(u) > 0 for large |u|.  2002 IMACS. Published by Elsevier Science B.V. All rights reserved.