Solutions of general second order ODEs using direct block method of Runge-Kutta type
This paper presents a three point block variable step size method of Runge-Kutta type for solving general second order ordinary differential equations (ODEs). The block method is formulated using Lagrange interpolation polynomial. Most of the mathematical problems which involve higher order ODEs cou...
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| Format: | Article |
| Language: | English |
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Universiti Kebangsaan Malaysia
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/25207/ http://psasir.upm.edu.my/id/eprint/25207/1/25207.pdf |
| _version_ | 1848845246063968256 |
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| author | Mukhtar, Nur Zahidah Abdul Majid, Zanariah Ismail, Fudziah Suleiman, Mohamed |
| author_facet | Mukhtar, Nur Zahidah Abdul Majid, Zanariah Ismail, Fudziah Suleiman, Mohamed |
| author_sort | Mukhtar, Nur Zahidah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper presents a three point block variable step size method of Runge-Kutta type for solving general second order ordinary differential equations (ODEs). The block method is formulated using Lagrange interpolation polynomial. Most of the mathematical problems which involve higher order ODEs could be reduced to system of first order equations. The proposed method obtains the numerical solutions directly without reducing to first order systems of ODEs. The method is used to compute the solutions at three points simultaneously by integrating the coefficients over the closest point in the block. The stability region of the block method is also studied. The numerical results obtained shows that the proposed method is more efficient compared to existing block methods in terms of total steps and execution time. |
| first_indexed | 2025-11-15T08:43:46Z |
| format | Article |
| id | upm-25207 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:43:46Z |
| publishDate | 2011 |
| publisher | Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-252072017-04-05T08:41:50Z http://psasir.upm.edu.my/id/eprint/25207/ Solutions of general second order ODEs using direct block method of Runge-Kutta type Mukhtar, Nur Zahidah Abdul Majid, Zanariah Ismail, Fudziah Suleiman, Mohamed This paper presents a three point block variable step size method of Runge-Kutta type for solving general second order ordinary differential equations (ODEs). The block method is formulated using Lagrange interpolation polynomial. Most of the mathematical problems which involve higher order ODEs could be reduced to system of first order equations. The proposed method obtains the numerical solutions directly without reducing to first order systems of ODEs. The method is used to compute the solutions at three points simultaneously by integrating the coefficients over the closest point in the block. The stability region of the block method is also studied. The numerical results obtained shows that the proposed method is more efficient compared to existing block methods in terms of total steps and execution time. Universiti Kebangsaan Malaysia 2011 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/25207/1/25207.pdf Mukhtar, Nur Zahidah and Abdul Majid, Zanariah and Ismail, Fudziah and Suleiman, Mohamed (2011) Solutions of general second order ODEs using direct block method of Runge-Kutta type. Journal of Quality Measurement and Analysis, 7 (2). pp. 145-154. ISSN 1823-5670 http://www.ukm.my/jqma/jqma7_2a.html |
| spellingShingle | Mukhtar, Nur Zahidah Abdul Majid, Zanariah Ismail, Fudziah Suleiman, Mohamed Solutions of general second order ODEs using direct block method of Runge-Kutta type |
| title | Solutions of general second order ODEs using direct block method of Runge-Kutta type |
| title_full | Solutions of general second order ODEs using direct block method of Runge-Kutta type |
| title_fullStr | Solutions of general second order ODEs using direct block method of Runge-Kutta type |
| title_full_unstemmed | Solutions of general second order ODEs using direct block method of Runge-Kutta type |
| title_short | Solutions of general second order ODEs using direct block method of Runge-Kutta type |
| title_sort | solutions of general second order odes using direct block method of runge-kutta type |
| url | http://psasir.upm.edu.my/id/eprint/25207/ http://psasir.upm.edu.my/id/eprint/25207/ http://psasir.upm.edu.my/id/eprint/25207/1/25207.pdf |