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Type :thesis
Subject :QA Mathematics
Main Author :Mohd Hafizul Muhammad
Title :An efficient implementation technique for implicit Runge-Kutta Gauss methods in solving mathematical stiff problems
Place of Production :Tanjong Malim
Publisher :Fakulti Sains dan Matematik
Year of Publication :2018
Corporate Name :Universiti Pendidikan Sultan Idris
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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  other researchers as well as to some other implicit Runge-Kutta methods.  


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