  The properties of the Bigeometric or proportional derivative are presented
and discussed explicitly. Based on this derivative, the Bigeometric Taylor
theorem is worked out. As an application of this calculus, the Bigeometric
Runge-Kutta method is derived and is applied to academic examples, with known
closed form solutions, and a sample problem from mathematical modelling in
biology. The comparison of the results of the Bigeometric Runge-Kutta method
with the ordinary Runge-Kutta method shows that the Bigeometric Runge-Kutta
method is at least for a particular set of initial value problems superior with
respect to accuracy and computation time to the ordinary Runge-Kutta method.
