For certain operating conditions and reaction schemes, catalytic membrane reactors (CMRs) may present sharp concentration profiles in the membrane. Using conventional fixed grid methods for solving the model equations in such conditions may lead to inaccurate predictions of the reactor's performance. This is demonstrated for two reaction systems: A reversible arrow B (for which a semi-analytical solution is available) and A reversible arrow B + 3C (which describes the cyclohexane dehydrogenation). Simulation results obtained with a fixed grid method using finite differences are compared to those from an adaptive method using an algorithm based on interpolating wavelets. Showing higher accuracy and computational efficiency, the latter proved to be a useful tool in dealing with this kind of problems.