AbstractThe ozone‐decomposition flame has been studied by means of fourth‐ and second‐order accurate schemes. The fourth‐order methods include a method of lines, a time‐linearization algorithm, and a majorant operatorsplitting technique. The second‐order schemes include two time‐linearization methods which use different temporal approximations. It is shown that the fourth‐order techniques yield comparable results to those obtained with very accurate finite element and adaptive grid finite‐difference algorithms. The results of the second‐order methods are in good agreement with second‐order explicit predictor‐corrector methods but predict a lower flame speed than that obtained by means of fourth‐order techniques. It is also shown that the temporal approximations are not as important as the spatial approximations in flame propagation problems characterized by the presence of several small time scales.