Full text can be accessed at http://link.springer.com/article/10.1007/s13370-011-0007-0This paper is devoted to the development of numerical method to deal with convection diffusion problem with reaction term (CDR) and convection diffusion dominated problem (stiff chemical reaction). The technique is based on the unifying Eulerian–Lagrangian schemes (particle transport method) under the framework of operator splitting method. In the computational domain, the particle set is assigned to solve the convection reaction subproblem along the characteristic curves which are formed by convective velocity. At each time step, convection, diffusion and reaction terms are solved separately by assuming that each phenomenon occurs separately in a sequential fashion. Moreover, adaptivities and projection techniques are used to add particles in the regions of high gradients, discontinuities and transfer a solution from particle set onto grid point respectively. The numerical results show that the particle transport method has improved the solutions of CDR problems. Nevertheless, the method is time consuming when compared with other classical techniques e.g., method of lines.