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Numerical solution of first order initial value problem using 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method


Teh, Yuan Ying and Yaacob, Nazeeruddin (2013) Numerical solution of first order initial value problem using 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method. In: 20th National Symposium on Mathematical Sciences, 18–20 December 2012, Palm Garden Hotel, Putrajaya, Malaysia. (Unpublished)

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Abstract

In this paper, a new implicit Runge-Kutta method which based on a 7-point Gauss-Kronrod-Lobatto quadrature formula is developed.The resulting implicit method is a 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method, or in brief as GKLM(7,10)-IIIA. GKLM(7,10)-IIIA requires seven function of evaluations at each integration step and it gives accuracy of order ten.In addition, GKLM(7,10)-IIIA has stage order seven and being A-stable. Numerical experiments compare the accuracy between GKLM(7,10)-IIIA and the classical 5-stage tenth order Gauss-Legendre method in solving some test problems. Numerical results reveal that GKLM(7,10)-IIIA is more accurate than the 5-stage tenth order Gauss-Legendre method because GKLM(7,10)-IIIA has higher stage order

Item Type: Conference or Workshop Item (Paper)
Additional Information: AIP Conf. Proc. 1522, 183 (2013), published by American Institute of Physics
Uncontrolled Keywords: Initial value problem,Gouss-Kronrod-lobatto quadrature formula, Gauss-Kronrod-Lobatto IIIA method
Subjects: Q Science > QA Mathematics
Divisions: College of Arts and Sciences
Depositing User: Dr. Yuan Ying Teh
Date Deposited: 13 Nov 2014 01:04
Last Modified: 13 Nov 2014 01:04
URI: http://repo.uum.edu.my/id/eprint/12687

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