A new approach is described to the evaluation of the quantum scattering S-matrix in3Datom-diatom reactive collision. The theory is developed in terms of natural collision coordinates where thecoordinate reactionfulfills the same role as a time in a time-dependent scattering formulation. Having written the full wavefunction of the particles system in the coupled-channel representation we have proved that the3Dmulti-channel scattering problem can be reduced to the inelastic single-arrangement problem which is described by system of ordinary dierential equations (ODE) of second order. The system of coupled-channel second order ODEs exactly is reduced to the system of integro-dierential equations (IDE) of first order which is solved with the initial conditions. The problem of Koshi for the system of IDEs is proposed to be solved by the method of Runge-Kutta of fourth order. The detailed algorithm for parallel simulation of initial3Dscattering problem is proposed. In result of simulation of IDEs the full wavefunction and all S-matrix elements of reactive transitions and state-to-state cross section are obtained simultaneously without other extra calculations.
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