A new approach is described to the evaluation of the S-matrix in three-dimensional atom-diatom reactive quantum scattering theory. A theory based on natural collision coordinates is developed, where the reaction coordinate can be viewed as fulfilling the same role as time in a time-dependent formulation. By writing the full wavefunction in coupled-channel form it is proved that the 3D multi-channel quantum reactive scattering problem can be treated in the same way as an inelastic single-arrangement problem. In particularly in the work two type coupled-channel representations, which lead to to two different systems of coupled-channel differential equations. The first system of coupledchannel equations is solved with the help of the R-matrix propagation method yielding simultaneously the full wavefunction and all S-matrix elements without further calculation. The second one is treated similarly. In this way we avoid a great volume of grid computations for 1D Schrödinger problem. The both algorithms use the intrinsic symmetry of scattering body-system, which allows to carry out maximally effective parallel computations of 3D scattering problem.