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Boundary-layer combustion, a major characteristic of a hybrid rocket engine, is a complex phenomenon of fluid dynamics and combustion. Its rate-limiting process is diffusion, whereas combustion reactions are generally very fast. One of numerical approaches for this is to solve simultaneously the Navier-Stokes equations with the transport equation for the mixture fraction. Chemical composition of the combustion gas can be determined by solving local chemical equilibrium for a given flow and mixture fraction fields. The governing equations for a diffusion-combustion flow with fast chemistry are characterized by the convective term, the diffusion term, and the chemical equilibrium calculation. As seen from the numerical methods for these, the convective-flux Jacobian and the numerical flux schemes, upwind higher precision approximation and limiter design, and chemical equilibrium calculation method. This study is focused especially on upwind higher precision approximation method. In this paper, by solving test problems such as quasi-one-dimensional hybrid rocket flow, assessment is made on a variety of numerical methods with respect to precision and convergence. [ABSTRACT FROM AUTHOR]