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

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

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...

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Bibliographic Details
Main Authors: Teh, Yuan Ying, Yaacob, Nazeeruddin
Format: Conference or Workshop Item
Language:English
Published: 2013
Subjects:
QA Mathematics
Online Access:https://repo.uum.edu.my/id/eprint/12695/1/Nu.pdf
Description
Summary: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

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