The Runge-Kutta interative algorithm is used to solve the standard propagation equations of fiber Raman amplifiers (FRAs). The analysis includes all the interactions of pumps, signals and noise without any approximation. Applications of the numerical analysis to practical FRA-based systems show a great reduction in computation time comparing with the direct integration approach based on ordinary coupled differential equations, while reproducing all the essential system performances precisely. In addition to enhanced computational efficiency, the derived equations can also give deeper insights into the detailed dynamics of FRAs. By making use of this method, flattened signal gains of a multiwavelength-pumping FRA with a bandwidth of over 100 nm are successfully calculated and pump power distributions along the transmission fiber are given. Futhermore, noise figures of the FRA are also presented. The method is very suitable to the engineering design of ultrabroad band FRAs with multiwavelength pumps.