Sin-Cos-Taylor-Like method for solving stiff ordinary diffrential equations
This paper discusses the derivation of an explicit Sin-Cos-Taylor-Like method for solving stiff ordinary differential equations, which is a formulation of the combination of a polynomial and the exponential function. This new method requires extra work to evaluate a number of differentiations of the...
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| Format: | Article |
| Language: | English |
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Ibnu Sina Institute for Fundamental Science Studies
2005
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| Online Access: | http://eprints.utm.my/81/ http://eprints.utm.my/81/1/jfs034043.pdf |
| _version_ | 1848889842715328512 |
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| author | Ahmad, Rokiah @ Rozita Yaacob, Nazeeruddin |
| author_facet | Ahmad, Rokiah @ Rozita Yaacob, Nazeeruddin |
| author_sort | Ahmad, Rokiah @ Rozita |
| building | UTeM Institutional Repository |
| collection | Online Access |
| description | This paper discusses the derivation of an explicit Sin-Cos-Taylor-Like method for solving stiff ordinary differential equations, which is a formulation of the combination of a polynomial and the exponential function. This new method requires extra work to evaluate a number of differentiations of the function involved. However, the result shows smaller errors when compared to the results from the explicit classical fourth-order Runge-Kutta (RK4) and the Adam- Bashforth-Moulton (ABM) methods. Implicit methods could work well for stiff problems but have certain drawbacks especially when discussing about the cost. Although extra work is required, this explicit method has its own advantages. Besides providing excellent results, the cost of computation using this explicit method is much cheaper than the implicit methods. We also considered the stability property for this method since the stability property of the classical explicit fourth order Runge-Kutta method is not adequate for the solution of stiff problems. As a result, we find that this explicit method is of order-6, which has been developed, and proved to be both A-stable and L-stable. |
| first_indexed | 2025-11-15T20:32:36Z |
| format | Article |
| id | utm-81 |
| institution | Universiti Teknologi Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T20:32:36Z |
| publishDate | 2005 |
| publisher | Ibnu Sina Institute for Fundamental Science Studies |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | utm-812017-02-08T01:41:50Z http://eprints.utm.my/81/ Sin-Cos-Taylor-Like method for solving stiff ordinary diffrential equations Ahmad, Rokiah @ Rozita Yaacob, Nazeeruddin QA Mathematics This paper discusses the derivation of an explicit Sin-Cos-Taylor-Like method for solving stiff ordinary differential equations, which is a formulation of the combination of a polynomial and the exponential function. This new method requires extra work to evaluate a number of differentiations of the function involved. However, the result shows smaller errors when compared to the results from the explicit classical fourth-order Runge-Kutta (RK4) and the Adam- Bashforth-Moulton (ABM) methods. Implicit methods could work well for stiff problems but have certain drawbacks especially when discussing about the cost. Although extra work is required, this explicit method has its own advantages. Besides providing excellent results, the cost of computation using this explicit method is much cheaper than the implicit methods. We also considered the stability property for this method since the stability property of the classical explicit fourth order Runge-Kutta method is not adequate for the solution of stiff problems. As a result, we find that this explicit method is of order-6, which has been developed, and proved to be both A-stable and L-stable. Ibnu Sina Institute for Fundamental Science Studies 2005-12 Article PeerReviewed application/pdf en http://eprints.utm.my/81/1/jfs034043.pdf Ahmad, Rokiah @ Rozita and Yaacob, Nazeeruddin (2005) Sin-Cos-Taylor-Like method for solving stiff ordinary diffrential equations. Journal of Fundamental Sciences, 1 . pp. 34-43. ISSN 1823-626X http://www.mjfas.utm.my/index.php/mjfas/article/view/13 |
| spellingShingle | QA Mathematics Ahmad, Rokiah @ Rozita Yaacob, Nazeeruddin Sin-Cos-Taylor-Like method for solving stiff ordinary diffrential equations |
| title | Sin-Cos-Taylor-Like method for solving stiff ordinary diffrential equations |
| title_full | Sin-Cos-Taylor-Like method for solving stiff ordinary diffrential equations |
| title_fullStr | Sin-Cos-Taylor-Like method for solving stiff ordinary diffrential equations |
| title_full_unstemmed | Sin-Cos-Taylor-Like method for solving stiff ordinary diffrential equations |
| title_short | Sin-Cos-Taylor-Like method for solving stiff ordinary diffrential equations |
| title_sort | sin-cos-taylor-like method for solving stiff ordinary diffrential equations |
| topic | QA Mathematics |
| url | http://eprints.utm.my/81/ http://eprints.utm.my/81/ http://eprints.utm.my/81/1/jfs034043.pdf |