Variable steps implicit block multistep method for solving first order ODEs
A new four-point implicit block multistep method is developed for solving systems of first-order ordinary differential equations with variable step size. The method computes the numerical solution at four equally spaced points simultaneously. The stability of the proposed method is investigated. The...
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| Format: | Article |
| Language: | English |
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Elsevier Science Publishers
2010
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| _version_ | 1796969293281230848 |
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| author | S., Mehrkanoon Abdul Majid, Zanariah Suleiman, Mohamed |
| author_facet | S., Mehrkanoon Abdul Majid, Zanariah Suleiman, Mohamed |
| author_sort | S., Mehrkanoon |
| collection | UPM |
| description | A new four-point implicit block multistep method is developed for solving systems of first-order ordinary differential equations with variable step size. The method computes the numerical solution at four equally spaced points simultaneously. The stability of the proposed method is investigated. The Gauss-Seidel approach is used for the implementation of the proposed method in the PE(CE)^m mode. The method is presented in a simple form of Adams type and all coefficients are stored in the code in order to avoid the calculation of divided difference and integration coefficients. Numerical examples are given to illustrate the efficiency of the proposed method. |
| first_indexed | 2024-03-06T07:40:51Z |
| format | Article |
| id | upm.eprints-17583 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T07:40:51Z |
| publishDate | 2010 |
| publisher | Elsevier Science Publishers |
| record_format | dspace |
| spelling | upm.eprints-175832012-12-17T01:46:26Z http://psasir.upm.edu.my/id/eprint/17583/ Variable steps implicit block multistep method for solving first order ODEs S., Mehrkanoon Abdul Majid, Zanariah Suleiman, Mohamed A new four-point implicit block multistep method is developed for solving systems of first-order ordinary differential equations with variable step size. The method computes the numerical solution at four equally spaced points simultaneously. The stability of the proposed method is investigated. The Gauss-Seidel approach is used for the implementation of the proposed method in the PE(CE)^m mode. The method is presented in a simple form of Adams type and all coefficients are stored in the code in order to avoid the calculation of divided difference and integration coefficients. Numerical examples are given to illustrate the efficiency of the proposed method. Elsevier Science Publishers 2010 Article PeerReviewed S., Mehrkanoon and Abdul Majid, Zanariah and Suleiman, Mohamed (2010) Variable steps implicit block multistep method for solving first order ODEs. Journal of Computational and Applied Mathematics, 233 (9). 2387 -2394. ISSN 0377-0427 http://dl.acm.org/citation.cfm?id=1698582 Differential equations - Numerical solutions Variables (Mathematics) 10.1016/j.cam.2009.10.023 English |
| spellingShingle | Differential equations - Numerical solutions Variables (Mathematics) S., Mehrkanoon Abdul Majid, Zanariah Suleiman, Mohamed Variable steps implicit block multistep method for solving first order ODEs |
| title | Variable steps implicit block multistep method for solving first order ODEs |
| title_full | Variable steps implicit block multistep method for solving first order ODEs |
| title_fullStr | Variable steps implicit block multistep method for solving first order ODEs |
| title_full_unstemmed | Variable steps implicit block multistep method for solving first order ODEs |
| title_short | Variable steps implicit block multistep method for solving first order ODEs |
| title_sort | variable steps implicit block multistep method for solving first order odes |
| topic | Differential equations - Numerical solutions Variables (Mathematics) |
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