Implicit two-point block method with third and fourth derivatives for solving general second order ODEs
In this paper we present an implicit two-point block method for solving directly the general second order ordinary differential equations (ODEs). The method incorporates the first and second derivatives of f(x; y; y 0), which are the third and fourth derivatives of the solution. The method is der...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Horizon Research Publishing
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/80180/ http://psasir.upm.edu.my/id/eprint/80180/1/Implicit%20Two-point%20block%20method%20with%20third%20and%20fourth%20Derivatives%20for%20Solving%20General%20Second%20Order%20ODEs.pdf |
| _version_ | 1848858849044332544 |
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| author | Allogmany, Reem Ayed Ismail, Fudziah Ibrahim, Zarina Bibi |
| author_facet | Allogmany, Reem Ayed Ismail, Fudziah Ibrahim, Zarina Bibi |
| author_sort | Allogmany, Reem Ayed |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper we present an implicit two-point block method for solving directly the general second order ordinary differential equations (ODEs). The method incorporates
the first and second derivatives of f(x; y; y 0), which are
the third and fourth derivatives of the solution. The method is
derived using Hermite Interpolating Polynomial as the basic
function. A performance comparison of the two-point block
method is compared in term of accuracy to several existing
methods, which have order almost equal or higher than that of the new method. Numerical results interpret the accuracy and efficacy of the new method. Application of the new method is discussed. |
| first_indexed | 2025-11-15T12:19:58Z |
| format | Article |
| id | upm-80180 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:19:58Z |
| publishDate | 2019 |
| publisher | Horizon Research Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-801802020-10-01T03:29:51Z http://psasir.upm.edu.my/id/eprint/80180/ Implicit two-point block method with third and fourth derivatives for solving general second order ODEs Allogmany, Reem Ayed Ismail, Fudziah Ibrahim, Zarina Bibi In this paper we present an implicit two-point block method for solving directly the general second order ordinary differential equations (ODEs). The method incorporates the first and second derivatives of f(x; y; y 0), which are the third and fourth derivatives of the solution. The method is derived using Hermite Interpolating Polynomial as the basic function. A performance comparison of the two-point block method is compared in term of accuracy to several existing methods, which have order almost equal or higher than that of the new method. Numerical results interpret the accuracy and efficacy of the new method. Application of the new method is discussed. Horizon Research Publishing 2019 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/80180/1/Implicit%20Two-point%20block%20method%20with%20third%20and%20fourth%20Derivatives%20for%20Solving%20General%20Second%20Order%20ODEs.pdf Allogmany, Reem Ayed and Ismail, Fudziah and Ibrahim, Zarina Bibi (2019) Implicit two-point block method with third and fourth derivatives for solving general second order ODEs. Mathematics and Statistics, 7 (4). pp. 116-123. ISSN 2332-2071; ESSN: 2332-2144 https://www.google.com/search?client=firefox-b-d&q=Implicit+Two-point+block+method+with+third+and+fourth+Derivatives+for+Solving+General+Second+Order+ODEs 10.13189/ms.2019.070404 |
| spellingShingle | Allogmany, Reem Ayed Ismail, Fudziah Ibrahim, Zarina Bibi Implicit two-point block method with third and fourth derivatives for solving general second order ODEs |
| title | Implicit two-point block method with third and fourth derivatives for solving general second order ODEs |
| title_full | Implicit two-point block method with third and fourth derivatives for solving general second order ODEs |
| title_fullStr | Implicit two-point block method with third and fourth derivatives for solving general second order ODEs |
| title_full_unstemmed | Implicit two-point block method with third and fourth derivatives for solving general second order ODEs |
| title_short | Implicit two-point block method with third and fourth derivatives for solving general second order ODEs |
| title_sort | implicit two-point block method with third and fourth derivatives for solving general second order odes |
| url | http://psasir.upm.edu.my/id/eprint/80180/ http://psasir.upm.edu.my/id/eprint/80180/ http://psasir.upm.edu.my/id/eprint/80180/ http://psasir.upm.edu.my/id/eprint/80180/1/Implicit%20Two-point%20block%20method%20with%20third%20and%20fourth%20Derivatives%20for%20Solving%20General%20Second%20Order%20ODEs.pdf |