We discuss some new approach for derivation of computational algorithms for certain types of evolution equations. The main idea of the algorithm is to make functional transformation of variables on the base of symmetry properties of pertinent physical system to make it quasi-diagonal. The approach is illustrated with the help of two important examples - the scattering in molecular system with elementary chemical reactions and the system of chemical kinetics for the many components system. The use of proposed approach show substantial speed-up over the standard algorithms and seems to be more effective with the increase of the size of the problem.