Numerical solution of first order initial value problem using 5-stage eight order Gauss-Kronrod method
In this paper, a new implicit Runge-Kutta method which based on a 5-point Gauss-Kronrod quadrature formula was developed. The resulting implicit method is a 5-stage eighth order Gauss-Kronrod method, or in brief as GKM(5,8). GKM(5,8) has stage order 5 and it is A-stable. Numerical experimentations h...
| Main Authors: | , |
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| Format: | Conference or Workshop Item |
| Language: | English |
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2011
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| Online Access: | https://repo.uum.edu.my/id/eprint/4811/1/Teh.pdf |
| _version_ | 1825740379958280192 |
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| author | Teh, Yuan Ying Yaacob, Nazeeruddin |
| author_facet | Teh, Yuan Ying Yaacob, Nazeeruddin |
| author_sort | Teh, Yuan Ying |
| collection | UUM |
| description | In this paper, a new implicit Runge-Kutta method which based on a 5-point Gauss-Kronrod quadrature formula was developed. The resulting implicit method is a 5-stage eighth order Gauss-Kronrod method, or in brief as GKM(5,8). GKM(5,8) has stage order 5 and it is A-stable. Numerical experimentations have compared the accuracy between GKM(5,8) and the 4-stage eighth order Gauss-Legendre method. Numerical results have showed that GKM (5,8) is more accurate than 4-stage eighth order Gauss-Legendre method because GKM (5,8) has higher stage order. |
| first_indexed | 2024-07-04T05:26:01Z |
| format | Conference or Workshop Item |
| id | uum-4811 |
| institution | Universiti Utara Malaysia |
| language | English |
| last_indexed | 2024-07-04T05:26:01Z |
| publishDate | 2011 |
| record_format | eprints |
| spelling | uum-48112012-02-25T05:49:05Z https://repo.uum.edu.my/id/eprint/4811/ Numerical solution of first order initial value problem using 5-stage eight order Gauss-Kronrod method Teh, Yuan Ying Yaacob, Nazeeruddin QA Mathematics In this paper, a new implicit Runge-Kutta method which based on a 5-point Gauss-Kronrod quadrature formula was developed. The resulting implicit method is a 5-stage eighth order Gauss-Kronrod method, or in brief as GKM(5,8). GKM(5,8) has stage order 5 and it is A-stable. Numerical experimentations have compared the accuracy between GKM(5,8) and the 4-stage eighth order Gauss-Legendre method. Numerical results have showed that GKM (5,8) is more accurate than 4-stage eighth order Gauss-Legendre method because GKM (5,8) has higher stage order. 2011-11-09 Conference or Workshop Item PeerReviewed application/pdf en https://repo.uum.edu.my/id/eprint/4811/1/Teh.pdf Teh, Yuan Ying and Yaacob, Nazeeruddin (2011) Numerical solution of first order initial value problem using 5-stage eight order Gauss-Kronrod method. In: Simposium Kebangsaan Sains Matematik (SKSM 19), 09-11 November 2011, UiTM Pulau Pinang. |
| spellingShingle | QA Mathematics Teh, Yuan Ying Yaacob, Nazeeruddin Numerical solution of first order initial value problem using 5-stage eight order Gauss-Kronrod method |
| title | Numerical solution of first order initial value problem using 5-stage eight order Gauss-Kronrod method |
| title_full | Numerical solution of first order initial value problem using 5-stage eight order Gauss-Kronrod method |
| title_fullStr | Numerical solution of first order initial value problem using 5-stage eight order Gauss-Kronrod method |
| title_full_unstemmed | Numerical solution of first order initial value problem using 5-stage eight order Gauss-Kronrod method |
| title_short | Numerical solution of first order initial value problem using 5-stage eight order Gauss-Kronrod method |
| title_sort | numerical solution of first order initial value problem using 5 stage eight order gauss kronrod method |
| topic | QA Mathematics |
| url | https://repo.uum.edu.my/id/eprint/4811/1/Teh.pdf |
| work_keys_str_mv | AT tehyuanying numericalsolutionoffirstorderinitialvalueproblemusing5stageeightordergausskronrodmethod AT yaacobnazeeruddin numericalsolutionoffirstorderinitialvalueproblemusing5stageeightordergausskronrodmethod |