{"id":9346,"date":"2024-10-22T09:53:18","date_gmt":"2024-10-22T08:53:18","guid":{"rendered":"https:\/\/icertpublication.com\/?page_id=9346"},"modified":"2024-10-25T10:03:12","modified_gmt":"2024-10-25T09:03:12","slug":"a-4-step-chebyshev-based-multiderivative-direct-solver-for-third-order-ordinary-differential-equations","status":"publish","type":"page","link":"https:\/\/icertpublication.com\/index.php\/edu-mania\/edumania-vol-02-issue-04\/a-4-step-chebyshev-based-multiderivative-direct-solver-for-third-order-ordinary-differential-equations\/","title":{"rendered":"A-4 Step Chebyshev Based Multiderivative Direct Solver For Third Order Ordinary Differential Equations"},"content":{"rendered":"\t\t
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A-4 Step Chebyshev Based Multiderivative Direct Solver For Third Order Ordinary Differential Equations\n<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Ogunlaran, O.M<\/span>1<\/span><\/span><\/p>

1<\/span><\/span>Mathematics Programme, College of Agriculture, Engineering and Science, Bowen University, Iwo, Osun State, Nigeria.<\/span><\/p>

Kehinde, M.A<\/span>2<\/span><\/span><\/p>

2<\/span><\/span>Department of Mathematics, Federal College of Education (Special), Oyo, Nigeria.<\/span><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Abstract\n<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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This paper develops and examines a uniform order, 4 step block method with Chebyshev series as bases function. Collocation and interpolation technique was used to modeled implicit discrete schemes from continuous scheme to derive our block. The block method obtained was of order 4. It is consistent, zero stable and consequently zero stable.\u00a0 The results obtained from four test problems shown that the method converges to exact solutions and perform better than some existing methods in the literatures.<\/span><\/p>

Keywords:<\/span> Multiderivative, Chebyshev series, Continuous Scheme, Direct solver.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Impact statement<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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This research presents a novel 4-step Chebyshev-based method for solving third-order ordinary differential equations (ODEs), offering an efficient and accurate approach for tackling complex problems in various fields, such as physics, engineering, and applied mathematics. The proposed method:<\/span><\/p>\n

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– Improves accuracy by utilizing Chebyshev polynomials to approximate solutions<\/span><\/p>\n

– Provides a reliable and robust tool for solving third-order ODEs, which are commonly encountered in modeling real-world phenomena<\/span><\/p>\n

 <\/b><\/p>\n

The impact of this research is two fold:<\/span><\/p>\n

1. Advancements in numerical analysis: This method contributes to the development of more efficient and accurate numerical techniques for solving ODEs, pushing the boundaries of computational mathematics.<\/span><\/p>\n

2. Practical applications: The proposed method can be applied to various fields, such as:<\/span><\/p>\n

– Physics: Modeling complex systems, like chaotic dynamics or quantum mechanics<\/span><\/p>\n

– Engineering: Optimizing systems, like control systems or electronic circuits<\/span><\/p>\n

\n<\/p>

– Applied mathematics: Solving problems in fluid dynamics, thermodynamics, or biomechanics<\/span><\/p>\n

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About the Author<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Prof. O.M. Ogunlaran is a Professor of Numerical Analysis at\u00a0 Mathematics ProgramCollege of Agriculture, Engineering and Science of Bowen University, Iwo, Nigeria. He decades of experience in teaching of applied Mathematics at various levels of degree. He has supervised several 1st degree, M.Sc and Ph.D students in Numerical Analysis. He has several international and national conferences experience and publications to his credit.<\/span><\/p>

\u00a0<\/span><\/p>

Dr. M.A. Kehinde is Ph.D holder of Numerical Analysis. He is a teaches Mathematics and Mathematics education at both NCE and degree level at Federal College of Education (Special), Oyo. He has several international and national conferences and publications<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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References: <\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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\u00a0<\/p>

  1. A Wiley-Inter Science Publication.<\/span><\/p><\/li>

  2. Ademola, M. B. (2017). <\/span>A sixth order Multi- derivative block method using Legendre polynomial for the solution of third order ordinary differential equations<\/span> (pp. 225\u2013233). Proceeding of Mathemataics Association of Nigeria.<\/span><\/p><\/li>

  3. Adeniran, A. O., & Longe, I. O. (2019). Solving directly second order initial value problems with Lucas polynomial. <\/span>Journal of Advances in Mathematics and Computer Science<\/span>, <\/span>32<\/span>(4), 1\u20137. <\/span>https:\/\/doi.org\/10.9734\/jamcs\/2019\/v32i430152<\/span><\/a><\/p><\/li>

  4. Adeniyi, R. B., & Mohammed, U. (2014). <\/span>A three step implicit hybrid linear MultistepMethod for solution of third order ordinary differential equations<\/span>, <\/span>25<\/span>(1) (pp. 62\u201374). ICSRS Publication.<\/span><\/p><\/li>

  5. Adeyeye, O., & Zurni, O. (2019). <\/span>Solving 3rd Order Ordinary Differential Equations using one-step block method with 4 equidistance generalized hybrid points. I AEng international journal of applied mathematics<\/span>.<\/span><\/p><\/li>

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  7. Anake, T. A., Odesanya, G. J., Oghonyan, G. J., & Agarana, M. C. (2013). Block algorithm for general third order ordinary differential equation. <\/span>ICASTOR Journal of Mathematical Sciences<\/span>, <\/span>7<\/span>(2), 127\u2013136.<\/span><\/p><\/li>

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  14. Guler, C., Kaya, S. O., & Sezer, M. (2019). Numerical Solutionof a Class of nonlinear Ordinary Differential Equations inHermite series. <\/span>Thermal Science<\/span> [International scientific journal], 1205\u20131210.<\/span><\/p><\/li>

  15. Jator, S. N. (2001). Improvements in Adams-Moulton methods for the first order initial value problems. <\/span>Journal of the Tennessee Academy of Science<\/span>, <\/span>76<\/span>(2), 57\u201360.<\/span><\/p><\/li>

  16. Jator, S. N. (2007). A sixth order linear multistep method for the direct solution of y\u2033 = f(x, y, y\u2032). <\/span>International Journal of Pure and Applied Mathematics<\/span>, <\/span>40<\/span>(4), 457\u2013472.<\/span><\/p><\/li>

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  19. Kuboye, J. O., Quadri, O. F., & Elusakin. (2020). Solving third order Ordinary Differential Equations directly using hybrid numerical Models. <\/span>Journal of Nigerian Society of Physical Science<\/span>, <\/span>2<\/span>, 69\u201376.<\/span><\/p><\/li>

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  22. Obarhua, F. O., & Kayode, S. J. (2016). Symmetric hybrid linear multistep method for General Third Oreder ordinary differential equations. <\/span>Open Access Library Journal<\/span>, <\/span>3<\/span>, e2583.\u00a0<\/span>http:\/\/doi.org\/10.4236\/0alib.1102583<\/span><\/a><\/p><\/li>

  23. Olabode, B. T. (2013). Block multistep method for Direct solution of Third order Ordinary Differential Equations. <\/span>FUTA Journal of Research in Sciences<\/span>, <\/span>2<\/span>, 194\u2013200.<\/span><\/p><\/li>

  24. Ramos, H., Jator, S. N., & Modebei, M. I. (2020). Efficient K-step Linear Block Methods to solve second order Initial Value Problems directly. <\/span>Mathematics<\/span>, <\/span>8<\/span>(10). <\/span>https:\/\/doi.org\/10.3390\/math8101752<\/span><\/a><\/p><\/li>

  25. Singla, R., Singh, G., Kanwar, V., & Ramos, H. (2021). Efficient adaptive step-size formulation of an optimized two- step hybrid method for directly solving general second order Initial Value Problems. <\/span>SociedadeBrasileira de Mathematica aplicada e computacional<\/span>.<\/span><\/p><\/li>

  26. Yahyah, Y. A., & Badmus, A. M. (2007). A 4. 3- step hybrid collocation method for special third order initial value problems of ODEs. <\/span>International Journal of Numerical Mathematics<\/span>, <\/span>3<\/span>, 306\u2013314.<\/span><\/p><\/li>

  27. Kumar, S., & Simran. (2024). Equity in K-12 STEAM education. <\/span>Eduphoria<\/span>, <\/span>02<\/span>(03), 49\u201355. https:\/\/doi.org\/10.59231\/eduphoria\/230412<\/span><\/p><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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    A-4 Step Chebyshev Based Multiderivative Direct Solver For Third Order Ordinary Differential Equations Ogunlaran, O.M1 1Mathematics Programme, College of Agriculture, Engineering and Science, Bowen University, Iwo, Osun State, Nigeria. Kehinde, M.A2 2Department of Mathematics, Federal College of Education (Special), Oyo, Nigeria. Abstract This paper develops and examines a uniform order, 4 step block method with […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":9298,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"no-sidebar","site-content-layout":"page-builder","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-9346","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/pages\/9346","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/comments?post=9346"}],"version-history":[{"count":13,"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/pages\/9346\/revisions"}],"predecessor-version":[{"id":9472,"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/pages\/9346\/revisions\/9472"}],"up":[{"embeddable":true,"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/pages\/9298"}],"wp:attachment":[{"href":"https:\/\/icertpublication.com\/index.php\/wp-json\/wp\/v2\/media?parent=9346"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}