[en] Some elements which are essential for the practical application of the step function perturbative numerical methods (SFPNM) are presented. They include: (i) the formulas of the solutions at any point of the integration domain, (not only at the mesh points as in the previous papers); (ii) the algorithm for backwards integration; (iii) analytic formulas for the derivatives of the computed solutions and for the integrals of the products of solutions; (iv) reliable rules for choosing step sizes consistent with a predetermined accuracy. Some illustrating experimental tests are reported in the last section. They prove, among others, that the SFPNM's are much faster than the method of Gordon. (author)