Coherent hybrid block method for approximating fourth-order ordinary differential equations
Conventionally, the most used method of solving fourth-order initial value problems of ordinary differential is to first reduce to a system of first-order differential equations. This approach affects the effectiveness and convergence of the numerical method due to the transformation. This paper com...
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| Format: | Article |
| Language: | English |
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Amasya University
2023-07-01
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| Series: | Journal of Amasya University the Institute of Sciences and Technology |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3001749 |
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| author | Jafaar Lawal Abdulmalik Oyedeji Abdulazeez Kayode Jimoh Faruk Muritala Muideen Ogunniran |
| author_facet | Jafaar Lawal Abdulmalik Oyedeji Abdulazeez Kayode Jimoh Faruk Muritala Muideen Ogunniran |
| author_sort | Jafaar Lawal |
| collection | DOAJ |
| description | Conventionally, the most used method of solving fourth-order initial value problems of ordinary differential is to first reduce to a system of first-order differential equations. This approach affects the effectiveness and convergence of the numerical method due to the transformation. This paper comprises the derivation, analysis, and implementation of a new hybrid block method for direct solution of fourth-order equations. The method is derived by collocation and interpolation of an assumed basis function. The basic properties of the block method, including zero stability, error constants, consistency, order, and convergence, were analyzed. From the analysis, the block method derived was found to be zero-stable, consistent, and convergent. Errors were computed for the proposed method, and they were proven to produce approximations that agree with exact solutions and as such this shows improvement with those of existing works. |
| format | Article |
| id | doaj-art-28bd95663c81470288563d1c1c33917f |
| institution | OA Journals |
| issn | 2717-8900 |
| language | English |
| publishDate | 2023-07-01 |
| publisher | Amasya University |
| record_format | Article |
| series | Journal of Amasya University the Institute of Sciences and Technology |
| spelling | doaj-art-28bd95663c81470288563d1c1c33917f2025-08-20T02:17:36ZengAmasya UniversityJournal of Amasya University the Institute of Sciences and Technology2717-89002023-07-0141527110.54559/jauist.126299436Coherent hybrid block method for approximating fourth-order ordinary differential equationsJafaar Lawal0https://orcid.org/0000-0001-6127-8274Abdulmalik Oyedeji1https://orcid.org/0000-0001-9677-3400Abdulazeez Kayode Jimoh2https://orcid.org/0000-0001-5850-5544Faruk Muritala3https://orcid.org/0000-0002-5857-9874Muideen Ogunniran4https://orcid.org/0000-0003-4510-1254Kwara State UniversityFederal University of Technology MinnaKwara State UniversityKwara State UniversityOsun State University, Osogbo NigeriaConventionally, the most used method of solving fourth-order initial value problems of ordinary differential is to first reduce to a system of first-order differential equations. This approach affects the effectiveness and convergence of the numerical method due to the transformation. This paper comprises the derivation, analysis, and implementation of a new hybrid block method for direct solution of fourth-order equations. The method is derived by collocation and interpolation of an assumed basis function. The basic properties of the block method, including zero stability, error constants, consistency, order, and convergence, were analyzed. From the analysis, the block method derived was found to be zero-stable, consistent, and convergent. Errors were computed for the proposed method, and they were proven to produce approximations that agree with exact solutions and as such this shows improvement with those of existing works.https://dergipark.org.tr/en/download/article-file/3001749hybrid methodsblock methodlinear stabilityerrors |
| spellingShingle | Jafaar Lawal Abdulmalik Oyedeji Abdulazeez Kayode Jimoh Faruk Muritala Muideen Ogunniran Coherent hybrid block method for approximating fourth-order ordinary differential equations Journal of Amasya University the Institute of Sciences and Technology hybrid methods block method linear stability errors |
| title | Coherent hybrid block method for approximating fourth-order ordinary differential equations |
| title_full | Coherent hybrid block method for approximating fourth-order ordinary differential equations |
| title_fullStr | Coherent hybrid block method for approximating fourth-order ordinary differential equations |
| title_full_unstemmed | Coherent hybrid block method for approximating fourth-order ordinary differential equations |
| title_short | Coherent hybrid block method for approximating fourth-order ordinary differential equations |
| title_sort | coherent hybrid block method for approximating fourth order ordinary differential equations |
| topic | hybrid methods block method linear stability errors |
| url | https://dergipark.org.tr/en/download/article-file/3001749 |
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