Comparison of one-step and two-step symmetrization in the variable stepsize setting
In this paper, we study the effects of symmetrization by the implicit midpoint rule (IMR) and the implicit trapezoidal rule (ITR) on the numerical solution of ordinary differential equations. We extend the study of the well-known formula of Gragg to a two-step symmetrizer and compare the efficiency...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2018
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| Online Access: | http://journalarticle.ukm.my/12675/ http://journalarticle.ukm.my/12675/1/36%20N.%20Razali.pdf |
| _version_ | 1848813066980950016 |
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| author | N. Razali, Zulkifli Mohd Nopiah, H. Othman, |
| author_facet | N. Razali, Zulkifli Mohd Nopiah, H. Othman, |
| author_sort | N. Razali, |
| building | UKM Institutional Repository |
| collection | Online Access |
| description | In this paper, we study the effects of symmetrization by the implicit midpoint rule (IMR) and the implicit trapezoidal rule (ITR) on the numerical solution of ordinary differential equations. We extend the study of the well-known formula of Gragg to a two-step symmetrizer and compare the efficiency of their use with the IMR and ITR. We present the experimental results on nonlinear problem using variable stepsize setting and the results show greater efficiency of the two-step symmetrizers over the one-step symmetrizers of IMR and ITR. |
| first_indexed | 2025-11-15T00:12:17Z |
| format | Article |
| id | oai:generic.eprints.org:12675 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T00:12:17Z |
| publishDate | 2018 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org:126752019-03-17T11:48:18Z http://journalarticle.ukm.my/12675/ Comparison of one-step and two-step symmetrization in the variable stepsize setting N. Razali, Zulkifli Mohd Nopiah, H. Othman, In this paper, we study the effects of symmetrization by the implicit midpoint rule (IMR) and the implicit trapezoidal rule (ITR) on the numerical solution of ordinary differential equations. We extend the study of the well-known formula of Gragg to a two-step symmetrizer and compare the efficiency of their use with the IMR and ITR. We present the experimental results on nonlinear problem using variable stepsize setting and the results show greater efficiency of the two-step symmetrizers over the one-step symmetrizers of IMR and ITR. Penerbit Universiti Kebangsaan Malaysia 2018-11 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/12675/1/36%20N.%20Razali.pdf N. Razali, and Zulkifli Mohd Nopiah, and H. Othman, (2018) Comparison of one-step and two-step symmetrization in the variable stepsize setting. Sains Malaysiana, 47 (11). pp. 2927-2932. ISSN 0126-6039 http://www.ukm.my/jsm/malay_journals/jilid47bil11_2018/KandunganJilid47Bil11_2018.html |
| spellingShingle | N. Razali, Zulkifli Mohd Nopiah, H. Othman, Comparison of one-step and two-step symmetrization in the variable stepsize setting |
| title | Comparison of one-step and two-step symmetrization
in the variable stepsize setting |
| title_full | Comparison of one-step and two-step symmetrization
in the variable stepsize setting |
| title_fullStr | Comparison of one-step and two-step symmetrization
in the variable stepsize setting |
| title_full_unstemmed | Comparison of one-step and two-step symmetrization
in the variable stepsize setting |
| title_short | Comparison of one-step and two-step symmetrization
in the variable stepsize setting |
| title_sort | comparison of one-step and two-step symmetrization
in the variable stepsize setting |
| url | http://journalarticle.ukm.my/12675/ http://journalarticle.ukm.my/12675/ http://journalarticle.ukm.my/12675/1/36%20N.%20Razali.pdf |