This research is aimed to produce an efficient implementation technique for the 2-stage (G2) and 3-stage (G3) implicit Runge-Kutta Gauss methods in solving mathematical stiff problems.   Both methods are constructed by using Maple software and have been implemented by using Matlab  software numerically.  This research applied four imple- mentation strategies which are full Newton  without compensated summation (FNWSN), full Newton with compensated summation (FNCS), simplified  Newton without com- pensated summation (SNWCS) and simplified Newton with compensated summation  (SNCS). Comparison have been done with the implementations of Hairer and Wanner scheme, Cooper and  Butcher scheme, and González scheme. Results for stiff test prob- lems showed that SNCS is the most  efficient technique in solving some real life mathe- matical problems such as the Kepler,  Oregonator, Van der Pol, HIRES and Brusselator problems.  According to the numerical results, the  impleme.....

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