Numerical algorithm of block method for general second order ODEs using variable step size
This paper outlines an alternative algorithm for solving general second order ordinary differential equations (ODEs). Normally, the numerical method was designed for solving higher order ODEs by converting it into an n-dimensional first order equations with implementation of constant step length. Ne...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2017
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| Online Access: | http://journalarticle.ukm.my/11070/ http://journalarticle.ukm.my/11070/1/16%20Nazreen%20Waeleh.pdf |
| _version_ | 1848812604652257280 |
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| author | Nazreen Waeleh, Zanariah Abdul Majid, |
| author_facet | Nazreen Waeleh, Zanariah Abdul Majid, |
| author_sort | Nazreen Waeleh, |
| building | UKM Institutional Repository |
| collection | Online Access |
| description | This paper outlines an alternative algorithm for solving general second order ordinary differential equations (ODEs). Normally, the numerical method was designed for solving higher order ODEs by converting it into an n-dimensional first order equations with implementation of constant step length. Nevertheless, this involved a lot of computational complexity which led to consumption a lot of time. Consequently, a direct block multistep method with utilization of variable step size strategy is proposed. This method was developed for computing the solution at four points simultaneously and the derivation based on numerical integration as well as using interpolation approach. The convergence of the proposed method is justified under suitable conditions of stability and consistency. Five numerical examples are considered and some comparisons are made with the existing methods for demonstrating the validity and reliability of the proposed algorithm. |
| first_indexed | 2025-11-15T00:04:56Z |
| format | Article |
| id | oai:generic.eprints.org:11070 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T00:04:56Z |
| publishDate | 2017 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org:110702017-12-12T04:49:04Z http://journalarticle.ukm.my/11070/ Numerical algorithm of block method for general second order ODEs using variable step size Nazreen Waeleh, Zanariah Abdul Majid, This paper outlines an alternative algorithm for solving general second order ordinary differential equations (ODEs). Normally, the numerical method was designed for solving higher order ODEs by converting it into an n-dimensional first order equations with implementation of constant step length. Nevertheless, this involved a lot of computational complexity which led to consumption a lot of time. Consequently, a direct block multistep method with utilization of variable step size strategy is proposed. This method was developed for computing the solution at four points simultaneously and the derivation based on numerical integration as well as using interpolation approach. The convergence of the proposed method is justified under suitable conditions of stability and consistency. Five numerical examples are considered and some comparisons are made with the existing methods for demonstrating the validity and reliability of the proposed algorithm. Penerbit Universiti Kebangsaan Malaysia 2017-05 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/11070/1/16%20Nazreen%20Waeleh.pdf Nazreen Waeleh, and Zanariah Abdul Majid, (2017) Numerical algorithm of block method for general second order ODEs using variable step size. Sains Malaysiana, 46 (5). pp. 817-824. ISSN 0126-6039 http://www.ukm.my/jsm/english_journals/vol46num5_2017/contentsVol46num5_2017.html |
| spellingShingle | Nazreen Waeleh, Zanariah Abdul Majid, Numerical algorithm of block method for general second order ODEs using variable step size |
| title | Numerical algorithm of block method for general second
order ODEs using variable step size |
| title_full | Numerical algorithm of block method for general second
order ODEs using variable step size |
| title_fullStr | Numerical algorithm of block method for general second
order ODEs using variable step size |
| title_full_unstemmed | Numerical algorithm of block method for general second
order ODEs using variable step size |
| title_short | Numerical algorithm of block method for general second
order ODEs using variable step size |
| title_sort | numerical algorithm of block method for general second
order odes using variable step size |
| url | http://journalarticle.ukm.my/11070/ http://journalarticle.ukm.my/11070/ http://journalarticle.ukm.my/11070/1/16%20Nazreen%20Waeleh.pdf |