An efficient implementation technique for implicit Runge-Kutta Gauss methods in solving mathematical stiff problems
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 Matlabsoftware numerically. T...
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| Format: | thesis |
| Language: | eng |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://ir.upsi.edu.my/detailsg.php?det=5755 |
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| Summary: | 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 Matlabsoftware numerically. This research applied four imple- mentation strategies which are full Newtonwithout compensated summation (FNWSN), full Newton with compensated summation (FNCS), simplifiedNewton 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 andButcher scheme, and Gonzlez scheme. Results for stiff test prob- lems showed that SNCS is the mostefficient 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, theimplementation of G2 using SNCS by the Hairer and Wanner scheme is the most efficient technique forsolving Kepler and Brusselator problems, while SNCS by the Gonzlez scheme is the most efficienttechnique for solving other problems. On the contrary for G3, SNCS by the Hairer and Wanner schemegives the most efficient technique for solving Kepler and Van der Pol problems, while SNCS by theGonzlez scheme gives the most efficient technique for solving other problems. In conclusion, forboth G2 and G3 methods, SNCS plays an important role to improve the efficiency of implicitRunge-Kutta Gauss methods in solv- ing mathematical stiff problems. As for the implications, theimplementation technique used in this research can be extended during tertiary education on thesubject numer- ical ordinary differential equations that focusses on implementation schemes byotherresearchers as well as to some other implicit Runge-Kutta methods. |
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