UPSI Digital Repository (UDRep)
|Abstract : Universiti Pendidikan Sultan Idris|
|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
implementation of G2 using SNCS by the Hairer and Wanner scheme is the most efficient technique for
solving Kepler and Brusselator problems, while SNCS by the González scheme is the most efficient
technique for solving other problems. On the contrary for G3, SNCS by the Hairer and Wanner scheme
gives the most efficient technique for solving Kepler and Van der Pol problems, while SNCS by the
González scheme gives the most efficient technique for solving other problems. In conclusion, for
both G2 and G3 methods, SNCS plays an important role to improve the efficiency of implicit
Runge-Kutta Gauss methods in solv- ing mathematical stiff problems. As for the implications, the
implementation technique used in this research can be extended during tertiary education on the
subject numer- ical ordinary differential equations that focusses on implementation schemes by
researchers as well as to some other implicit Runge-Kutta methods.
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