A class of single-step hybrid block methods with equally spaced points for general third-order ordinary differential equations
This study presents a class of single-step, self-starting hybrid block methods for directly solving general third-order ordinary differential equations (ODEs) without reduction to first order equations. The methods are developed through interpolation and collocation at systematically selected evenl...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Nigerian Society of Physical Sciences
2023-11-01
|
| Series: | Journal of Nigerian Society of Physical Sciences |
| Subjects: | |
| Online Access: | https://journal.nsps.org.ng/index.php/jnsps/article/view/1484 |
| _version_ | 1797317289317498880 |
|---|---|
| author | Maduabuchi Gabriel Orakwelu Olumuyiwa Otegbeye Hermane Mambili-Mamboundou |
| author_facet | Maduabuchi Gabriel Orakwelu Olumuyiwa Otegbeye Hermane Mambili-Mamboundou |
| author_sort | Maduabuchi Gabriel Orakwelu |
| collection | DOAJ |
| description |
This study presents a class of single-step, self-starting hybrid block methods for directly solving general third-order ordinary differential equations (ODEs) without reduction to first order equations. The methods are developed through interpolation and collocation at systematically selected evenly spaced nodes with the aim of boosting the accuracy of the methods. The zero stability, consistency and convergence of the algorithms are established. Scalar and systems of linear and nonlinear ODEs are approximated to test the effectiveness of the schemes, and the results obtained are compared against other methods from the literature. Significantly, the study shows that an increase in the number of intra-step points improves the accuracy of the solutions obtained using the proposed methods.
|
| first_indexed | 2024-03-08T03:32:46Z |
| format | Article |
| id | doaj.art-f1a5672887c14016aa62ac82ecde6d3c |
| institution | Directory Open Access Journal |
| issn | 2714-2817 2714-4704 |
| language | English |
| last_indexed | 2024-03-08T03:32:46Z |
| publishDate | 2023-11-01 |
| publisher | Nigerian Society of Physical Sciences |
| record_format | Article |
| series | Journal of Nigerian Society of Physical Sciences |
| spelling | doaj.art-f1a5672887c14016aa62ac82ecde6d3c2024-02-10T16:27:50ZengNigerian Society of Physical SciencesJournal of Nigerian Society of Physical Sciences2714-28172714-47042023-11-015410.46481/jnsps.2023.1484A class of single-step hybrid block methods with equally spaced points for general third-order ordinary differential equationsMaduabuchi Gabriel Orakwelu0Olumuyiwa Otegbeye1Hermane Mambili-Mamboundou2School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg, South Africa | DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa.School of Computer Science and Applied Mathematics, Faculty of Science, University of the Witwatersrand, Johannesburg, South AfricaSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg, South Africa This study presents a class of single-step, self-starting hybrid block methods for directly solving general third-order ordinary differential equations (ODEs) without reduction to first order equations. The methods are developed through interpolation and collocation at systematically selected evenly spaced nodes with the aim of boosting the accuracy of the methods. The zero stability, consistency and convergence of the algorithms are established. Scalar and systems of linear and nonlinear ODEs are approximated to test the effectiveness of the schemes, and the results obtained are compared against other methods from the literature. Significantly, the study shows that an increase in the number of intra-step points improves the accuracy of the solutions obtained using the proposed methods. https://journal.nsps.org.ng/index.php/jnsps/article/view/1484Third-orderHybrid block methodConvergenceInitial and boundary value problems |
| spellingShingle | Maduabuchi Gabriel Orakwelu Olumuyiwa Otegbeye Hermane Mambili-Mamboundou A class of single-step hybrid block methods with equally spaced points for general third-order ordinary differential equations Journal of Nigerian Society of Physical Sciences Third-order Hybrid block method Convergence Initial and boundary value problems |
| title | A class of single-step hybrid block methods with equally spaced points for general third-order ordinary differential equations |
| title_full | A class of single-step hybrid block methods with equally spaced points for general third-order ordinary differential equations |
| title_fullStr | A class of single-step hybrid block methods with equally spaced points for general third-order ordinary differential equations |
| title_full_unstemmed | A class of single-step hybrid block methods with equally spaced points for general third-order ordinary differential equations |
| title_short | A class of single-step hybrid block methods with equally spaced points for general third-order ordinary differential equations |
| title_sort | class of single step hybrid block methods with equally spaced points for general third order ordinary differential equations |
| topic | Third-order Hybrid block method Convergence Initial and boundary value problems |
| url | https://journal.nsps.org.ng/index.php/jnsps/article/view/1484 |
| work_keys_str_mv | AT maduabuchigabrielorakwelu aclassofsinglestephybridblockmethodswithequallyspacedpointsforgeneralthirdorderordinarydifferentialequations AT olumuyiwaotegbeye aclassofsinglestephybridblockmethodswithequallyspacedpointsforgeneralthirdorderordinarydifferentialequations AT hermanemambilimamboundou aclassofsinglestephybridblockmethodswithequallyspacedpointsforgeneralthirdorderordinarydifferentialequations AT maduabuchigabrielorakwelu classofsinglestephybridblockmethodswithequallyspacedpointsforgeneralthirdorderordinarydifferentialequations AT olumuyiwaotegbeye classofsinglestephybridblockmethodswithequallyspacedpointsforgeneralthirdorderordinarydifferentialequations AT hermanemambilimamboundou classofsinglestephybridblockmethodswithequallyspacedpointsforgeneralthirdorderordinarydifferentialequations |