[en] The method developed in the previous paper (preprint, C.I.Ph. (Bucharest), MC-2-78, 1978) is here investigated from computational point of view. Special emphasis is paid to the two basic descriptors of the efficiency: the volume of memory required and the computational effort (timing). Next, two experimental cases are reported. They (i) confirm the theoretical estimates for the rate cf convergence of each version of the present method and (ii) show that the present method is substantially faster than the others. Specifically, it is found that for typical physical problems it is faster by a factor of ten up to twenty than the methods commonly used, viz. Numerov and de Vogelaere. The data reported also allow an inUirect comparison with the method of Gordon. I l/ allow an indirect comparison with the method of Gordon. It is shown that, while this exhibits the same rate as our basic, lowest order version, the computational effort for the latter is, in case of systems with nine equations, only half than for the method of Gordon. At the end of the paper some types of physical problems are suggested which should be the most benefitting if solved numerically with the present method. (author)