Abstract An efficient numerical method for solution of boundary value problems with additional condition is presented. The approach is based on the shooting method but the procedure of seeking “the proper shot” allows one to satisfy “additional” boundary conditions. General considerations are illustrated by a real example. The computational example concerns the “dead zone” regime for the non-linear diffusion-reaction equation in heterogeneous catalysis. Accuracy and efficiency of the presented method confirm results obtained for a wide range of changes of process parameters, including the vicinity of a critical point. Calculations were performed with the use of the Maple® program.