A Chebyshev polynomial based block integrator for the direct numerical solution of fourth order ordinary differential equations
This paper introduces an innovative method for numerically integrating fourth-order initial value problems by utilizing Chebyshev polynomials as the fundamental basis function. The block integrator base on Chebyshev polynomial demonstrates significant improvements in accuracy and stability, renderi...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Nigerian Society of Physical Sciences
2024-03-01
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| Series: | Journal of Nigerian Society of Physical Sciences |
| Subjects: | |
| Online Access: | https://www.journal.nsps.org.ng/index.php/jnsps/article/view/1917 |
| _version_ | 1797208954038648832 |
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| author | Oladotun Ogunlaran Michael Kehinde Moses Akanbi Emmanuel Akinola |
| author_facet | Oladotun Ogunlaran Michael Kehinde Moses Akanbi Emmanuel Akinola |
| author_sort | Oladotun Ogunlaran |
| collection | DOAJ |
| description |
This paper introduces an innovative method for numerically integrating fourth-order initial value problems by utilizing Chebyshev polynomials as the fundamental basis function. The block integrator base on Chebyshev polynomial demonstrates significant improvements in accuracy and stability, rendering it a valuable tool across various scientific and engineering fields. By leveraging the characteristics of Chebyshev polynomials, this approach accurately estimates solutions for fourth-order differential equations without reducing it to a system of first order Ordinary Differential Equations while at the same time effectively managing error accumulation within a block integration framework and thereby enhancing its accuracy over extended intervals. Through rigorous numerical experiments, the effectiveness and reliability of the new integrator are demonstrated and compared with existing methods. The new method is consistent, zero stable and convergent. The method also shows an appreciable error constants. The new method performed better in terms of accuracy than the existing methods in the literature in both linear and nonlinear problems.
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| first_indexed | 2024-04-24T09:47:00Z |
| format | Article |
| id | doaj.art-cd8ade8b881d48cf810e13df8adb4392 |
| institution | Directory Open Access Journal |
| issn | 2714-2817 2714-4704 |
| language | English |
| last_indexed | 2024-04-24T09:47:00Z |
| publishDate | 2024-03-01 |
| publisher | Nigerian Society of Physical Sciences |
| record_format | Article |
| series | Journal of Nigerian Society of Physical Sciences |
| spelling | doaj.art-cd8ade8b881d48cf810e13df8adb43922024-04-14T17:38:01ZengNigerian Society of Physical SciencesJournal of Nigerian Society of Physical Sciences2714-28172714-47042024-03-016210.46481/jnsps.2024.1917A Chebyshev polynomial based block integrator for the direct numerical solution of fourth order ordinary differential equationsOladotun Ogunlaran0Michael Kehinde1Moses Akanbi2Emmanuel Akinola3Mathematics Programme, College of Agriculture, Engineering and Science, Bowen University, Iwo, NigeriaMathematics Programme, College of Agriculture, Engineering and Science, Bowen University, Iwo, NigeriaDepartment of Mathematics; and Africa Centre of Excellence for Innovative and Transformative STEM Education (ACEITSE), Lagos State University, Ojo, Lagos, NigeriaMathematics Programme, College of Agriculture, Engineering and Science, Bowen University, Iwo, Nigeria This paper introduces an innovative method for numerically integrating fourth-order initial value problems by utilizing Chebyshev polynomials as the fundamental basis function. The block integrator base on Chebyshev polynomial demonstrates significant improvements in accuracy and stability, rendering it a valuable tool across various scientific and engineering fields. By leveraging the characteristics of Chebyshev polynomials, this approach accurately estimates solutions for fourth-order differential equations without reducing it to a system of first order Ordinary Differential Equations while at the same time effectively managing error accumulation within a block integration framework and thereby enhancing its accuracy over extended intervals. Through rigorous numerical experiments, the effectiveness and reliability of the new integrator are demonstrated and compared with existing methods. The new method is consistent, zero stable and convergent. The method also shows an appreciable error constants. The new method performed better in terms of accuracy than the existing methods in the literature in both linear and nonlinear problems. https://www.journal.nsps.org.ng/index.php/jnsps/article/view/1917Chebyshev PolynomialContinuous schemeblock methodinitial value problems |
| spellingShingle | Oladotun Ogunlaran Michael Kehinde Moses Akanbi Emmanuel Akinola A Chebyshev polynomial based block integrator for the direct numerical solution of fourth order ordinary differential equations Journal of Nigerian Society of Physical Sciences Chebyshev Polynomial Continuous scheme block method initial value problems |
| title | A Chebyshev polynomial based block integrator for the direct numerical solution of fourth order ordinary differential equations |
| title_full | A Chebyshev polynomial based block integrator for the direct numerical solution of fourth order ordinary differential equations |
| title_fullStr | A Chebyshev polynomial based block integrator for the direct numerical solution of fourth order ordinary differential equations |
| title_full_unstemmed | A Chebyshev polynomial based block integrator for the direct numerical solution of fourth order ordinary differential equations |
| title_short | A Chebyshev polynomial based block integrator for the direct numerical solution of fourth order ordinary differential equations |
| title_sort | chebyshev polynomial based block integrator for the direct numerical solution of fourth order ordinary differential equations |
| topic | Chebyshev Polynomial Continuous scheme block method initial value problems |
| url | https://www.journal.nsps.org.ng/index.php/jnsps/article/view/1917 |
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