The issues of the large cell Reynolds number and large Damkohler number are examined. Thirteen finite-difference schemes for solving a system of highly nonlinear convection-diffusion-reaction integrodifferential equations are studied. The system models the propagation of a one-dimensional unsteady laminar flame in closed or open combustors. The numerical schemes include an explicit scheme with upwind, central, and hybrid differencing, a predictor-corrector explicit scheme, a sequential implicit scheme, a quasi-linear implicit scheme, a block implicit scheme, the standard Crank-Nicolson implicit scheme, two methods of lines, a projection implicit scheme, an operator-splitting scheme, and the QUICK scheme. The efficiency, accuracy, and stability of these schemes art discussed. In particular, it is shown that the treatment of convection terms and of reaction terms, as well as the flow conditions, has a strong impact on the selection of an optimum numerical technique. Generally, for a large Damkohler number the explicit methods are judged superior to the implicit methods. For a large cell Reynolds number, the QUICK scheme is the most promising.