Error estimation by using symmetrization and efficient implementation scheme for 3-stage Gauss method

Sara Syahrunnisaa Mustapha

Abstract

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 observed that GMR scheme is efficient by using the G3 method especially when the error estimation is obtained by using symmetrization technique instead of local extrapolation if compared with other schemes. In conclusion, GMR scheme is seen to be very robust in solving Robertson problem by the G3 method in terms of tolerance and computational time.

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