  The adiabatic approximation is well-known method for effective study of
few-body systems in molecular, atomic and nuclear physics, using the idea of
separation of "fast" and "slow" variables. The generalization of the standard
adiabatic ansatz for the case of multi-channel wave function when all variables
treated dynamically is presented.
  For this reason we are introducing the step-by-step averaging methods in
order to eliminate consequently from faster to slower variables. We present a
symbolic-numerical algorithm for reduction of multistep adiabatic equations,
corresponding to the MultiStep Generalization of Kantorovich Method, for
solving multidimensional boundary-value problems by finite element method. An
application of the algorithm to calculation of the ground and first exited
states of a Helium atom is given.
