A new formulae of variable step 3-point block BDF method for solving stiff ODEs
This paper derives a new variable step 3-point block method based on Backward Differentiation Formula (BDF) for solving stiff Ordinary Differential Equations (ODEs). The strategy involved in the developed method is to control the step size at each iteration to optimize the precision and produce thre...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Scientific Advances Publishers
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/36199/1/A%20new%20formulae%20of%20variable%20step%203.pdf |
| _version_ | 1796972862952701952 |
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| author | Abasi, Naghmeh Suleiman, Mohamed Ismail, Fudziah Ibrahim, Zarina Bibi Musa, Hamisu Abbasi, Neda |
| author_facet | Abasi, Naghmeh Suleiman, Mohamed Ismail, Fudziah Ibrahim, Zarina Bibi Musa, Hamisu Abbasi, Neda |
| author_sort | Abasi, Naghmeh |
| collection | UPM |
| description | This paper derives a new variable step 3-point block method based on Backward Differentiation Formula (BDF) for solving stiff Ordinary Differential Equations (ODEs). The strategy involved in the developed method is to control the step size at each iteration to optimize the precision and produce three solution values simultaneously at each step. The method is analyzed in having the conditions for zero stability and found to be of order 6. The stability regions of the method are also investigated and presented in distinct graphs. The proposed method is compared to MATLAB’s suite ODEs solvers, namely, ode15s and ode23s. Numerical results obtained are provided to support the enhancement of the method in terms of accuracy. |
| first_indexed | 2024-03-06T08:34:37Z |
| format | Article |
| id | upm.eprints-36199 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:34:37Z |
| publishDate | 2014 |
| publisher | Scientific Advances Publishers |
| record_format | dspace |
| spelling | upm.eprints-361992015-08-24T02:33:23Z http://psasir.upm.edu.my/id/eprint/36199/ A new formulae of variable step 3-point block BDF method for solving stiff ODEs Abasi, Naghmeh Suleiman, Mohamed Ismail, Fudziah Ibrahim, Zarina Bibi Musa, Hamisu Abbasi, Neda This paper derives a new variable step 3-point block method based on Backward Differentiation Formula (BDF) for solving stiff Ordinary Differential Equations (ODEs). The strategy involved in the developed method is to control the step size at each iteration to optimize the precision and produce three solution values simultaneously at each step. The method is analyzed in having the conditions for zero stability and found to be of order 6. The stability regions of the method are also investigated and presented in distinct graphs. The proposed method is compared to MATLAB’s suite ODEs solvers, namely, ode15s and ode23s. Numerical results obtained are provided to support the enhancement of the method in terms of accuracy. Scientific Advances Publishers 2014-08 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/36199/1/A%20new%20formulae%20of%20variable%20step%203.pdf Abasi, Naghmeh and Suleiman, Mohamed and Ismail, Fudziah and Ibrahim, Zarina Bibi and Musa, Hamisu and Abbasi, Neda (2014) A new formulae of variable step 3-point block BDF method for solving stiff ODEs. Journal of Pure and Applied Mathematics: Advances and Applications, 12 (1). pp. 49-76. ISSN 0974-9381 http://www.scientificadvances.co.in/artical/5/147 |
| spellingShingle | Abasi, Naghmeh Suleiman, Mohamed Ismail, Fudziah Ibrahim, Zarina Bibi Musa, Hamisu Abbasi, Neda A new formulae of variable step 3-point block BDF method for solving stiff ODEs |
| title | A new formulae of variable step 3-point block BDF method for solving stiff ODEs |
| title_full | A new formulae of variable step 3-point block BDF method for solving stiff ODEs |
| title_fullStr | A new formulae of variable step 3-point block BDF method for solving stiff ODEs |
| title_full_unstemmed | A new formulae of variable step 3-point block BDF method for solving stiff ODEs |
| title_short | A new formulae of variable step 3-point block BDF method for solving stiff ODEs |
| title_sort | new formulae of variable step 3 point block bdf method for solving stiff odes |
| url | http://psasir.upm.edu.my/id/eprint/36199/1/A%20new%20formulae%20of%20variable%20step%203.pdf |
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