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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| Format: | Conference or Workshop Item |
| Language: | English |
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2013
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| Online Access: | https://repo.uum.edu.my/id/eprint/12695/1/Nu.pdf |
| _version_ | 1803626462846124032 |
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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 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 |
| first_indexed | 2024-07-04T05:50:33Z |
| format | Conference or Workshop Item |
| id | uum-12695 |
| institution | Universiti Utara Malaysia |
| language | English |
| last_indexed | 2024-07-04T05:50:33Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | uum-126952014-11-13T01:00:08Z https://repo.uum.edu.my/id/eprint/12695/ Numerical solution of first order initial value problem using 4-stage sixth order Gauss-Kronrod-Radau IIA method Teh, Yuan Ying Yaacob, Nazeeruddin QA Mathematics 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 2013 Conference or Workshop Item PeerReviewed application/pdf en https://repo.uum.edu.my/id/eprint/12695/1/Nu.pdf 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. http://dx.doi.org/10.1063/1.4801121 doi:10.1063/1.4801121 doi:10.1063/1.4801121 |
| spellingShingle | QA Mathematics Teh, Yuan Ying Yaacob, Nazeeruddin Numerical solution of first order initial value problem using 4-stage sixth order Gauss-Kronrod-Radau IIA method |
| title | Numerical solution of first order initial value problem using 4-stage sixth order Gauss-Kronrod-Radau IIA method |
| title_full | Numerical solution of first order initial value problem using 4-stage sixth order Gauss-Kronrod-Radau IIA method |
| title_fullStr | Numerical solution of first order initial value problem using 4-stage sixth order Gauss-Kronrod-Radau IIA method |
| title_full_unstemmed | Numerical solution of first order initial value problem using 4-stage sixth order Gauss-Kronrod-Radau IIA method |
| title_short | Numerical solution of first order initial value problem using 4-stage sixth order Gauss-Kronrod-Radau IIA method |
| title_sort | numerical solution of first order initial value problem using 4 stage sixth order gauss kronrod radau iia method |
| topic | QA Mathematics |
| url | https://repo.uum.edu.my/id/eprint/12695/1/Nu.pdf |
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