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Numerical solution of first order initial value problem using 4-stage sixth order Gauss-Kronrod-Radau IIA method


Teh, Yuan Ying and Yaacob, Nazeeruddin (2013) Numerical solution of first order initial value problem using 4-stage sixth order Gauss-Kronrod-Radau IIA method. In: 20th National Symposium on Mathematical Sciences, 18–20 December 2012, Palm Garden Hotel, Putrajaya, Malaysia.

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Abstract

In this paper, a new implicit Runge-Kutta method which based on a 4-point Gauss-Kronrod-Radau II quadrature formula is developed.The resulting implicit method is a 4-stage sixth order Gauss-Kronrod-Radau IIA method, or in brief as GKRM(4,6)-IIA. GKRM(4,6)-IIA requires four function of evaluations at each integration step and it gives accuracy of order six.In addition, GKRM(4,6)-IIA has stage order four and being L-stable. Numerical experiments compare the accuracy between GKRM(4,6)-IIA and the classical 3-stage sixth order Gauss-Legendre method in solving some test problems. Numerical results reveal that GKRM(4,6)-IIA is more accurate than the 3-stage sixth order Gauss-Legendre method because GKRM(4,6)-IIA has higher stage order

Item Type: Conference or Workshop Item (Paper)
Additional Information: ISBN: 978-0-7354-1150-0 AIP Conf. Proc. 1522, 1 (2013)
Uncontrolled Keywords: Initial value problem; Gauss-Kronrod-Radau II quadrature formula; Gauss-Kronrod-Randau IIA method
Subjects: Q Science > QA Mathematics
Divisions: College of Arts and Sciences
Depositing User: Dr. Yuan Ying Teh
Date Deposited: 13 Nov 2014 01:00
Last Modified: 13 Nov 2014 01:00
URI: http://repo.uum.edu.my/id/eprint/12695

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