  This paper illuminates the derivation, the applicability, and the efficiency
of the Multiplicative Runge-Kutta Method, derived in the frame- work of
geometric multiplicative calculus. The removal of the restrictions of geometric
multiplicative calculus to positive-valued functions of real variable and the
fact that the multiplicative derivative does not exist at the roots of the
function, is presented explicitly to ensure that the proposed method is uni-
versally applicable. The error analysis is also carried out in the framework of
geometric multiplicative calculus explicitly. The presented method is applied
to various problems and the results are compared to the ones obtained from the
Ordinary Runge-Kutta Method. Moreover, for one example, a comparison of the
computation time vs. relative error, is worked out, to illustrate the general
advantage of the proposed method.
