The research is aimed to find the most efficient implementation strategies  by Gauss numerical   methods  for  solving  stiff  problems  and  the  best  error  estimation  in  the variable  stepsize setting. The numerical methods considered as a research methodology are  the  2-stage   (G2)  and  3-stage  (G3)  implicit  Runge-Kutta  Gauss  methods.  Two strategies  by Hairer  and   Wanner  (HW)  and  Gonzalez-Pinto,  Montijano  and  Randez (GMR)  schemes  were  implemented.  The   variable  stepsize  setting  employed  the simplified Newton is modified to fit according to HW and  GMR schemes in solving the nonlinear  algebraic  systems  of  the  equations.  The  error   estimation  for  the  variable stepsize setting is computed using extrapolation technique with stepsizes  h  and  h  2 . HW and GMR schemes used the transformation matrix T to improve the efficiency of the methods and  also compared with the mod.....

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This research focuses on the implementation strategies by the implicit Runge-Kutta Gauss methods in solving Robertson problem using variable stepsize setting. This research considers ideas of implementation strategies by Hairer and Wanner (HW) and Gonzalez-Pinto, Montijano and Randez (GMR) schemes that uses a certain transformation matrix T to improve the efficiency of the numerical methods. Both implementations use simplified Newton iterations to solve the nonlinear algebraic equations for the implicit methods. These implementation strategies are compared with the modified Hairer and Wanner (MHW) scheme without using any transformation matrix T. The numerical methods considered are the implicit 3-stage Gauss (G3) method of order-6. The numerical results are given for Robertson problem which is a chemical reaction stiff problem. The variable stepsize setting is adapted in Matlab code that estimates the error using symmetrization technique. Based on the numerical experiments, it is obse.....

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