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

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

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 evaluat...

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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/12687/1/Teh.pdf
Description
Summary: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

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