{"id":9346,"date":"2024-10-22T09:53:18","date_gmt":"2024-10-22T08:53:18","guid":{"rendered":"https:\/\/icertpublication.com\/?page_id=9346"},"modified":"2026-03-07T06:29:43","modified_gmt":"2026-03-07T00:59:43","slug":"a-4-step-chebyshev-based-multiderivative-direct-solver-for-third-order-ordinary-differential-equations","status":"publish","type":"page","link":"https:\/\/icert.org.in\/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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Edumania-An International Multidisciplinary Journal<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Vol-02, Issue-04 (Oct -Dec 2024)<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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An International scholarly\/ academic journal, peer-reviewed\/ refereed journal, ISSN : 2960-0006<\/h5>\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\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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DOI:\u00a0<\/span>https:\/\/doi.org\/10.59231\/edumania\/9070<\/span><\/a><\/p>

Page Number:\u00a0pp. 17-33<\/span><\/p>

Subject:\u00a0Numerical Analysis, Applied Mathematics, Differential Equations, Computational Methods<\/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

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Received:\u00a010 July 2024<\/span><\/p>

Accepted:\u00a003 August 2024<\/span><\/p>

Published:\u00a001 October 2024<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Thematic Classification:\u00a0Physical Sciences: Mathematics; Numerical Methods<\/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\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

 <\/b><\/p>\n

– 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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Cite this Article<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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APA (7th ed.):<\/span>\u00a0Ogunlaran, O. M., & Kehinde, M. A. (2024). A-4 Step Chebyshev Based Multiderivative Direct Solver For Third Order Ordinary Differential Equations.\u00a0<\/span>Edumania-An International Multidisciplinary Journal<\/span>,\u00a02(4), 17\u201333.\u00a0<\/span>https:\/\/doi.org\/10.59231\/edumania\/9070<\/span><\/a><\/p>

Chicago (17th ed.):<\/span>\u00a0Ogunlaran, O.M., and M.A. Kehinde. “A-4 Step Chebyshev Based Multiderivative Direct Solver For Third Order Ordinary Differential Equations.”\u00a0<\/span>Edumania-An International Multidisciplinary Journal<\/span>\u00a02, no. 4 (2024): 17\u201333.\u00a0<\/span>https:\/\/doi.org\/10.59231\/edumania\/9070<\/span><\/a>.<\/span><\/p>

MLA (9th ed.):<\/span>\u00a0Ogunlaran, O. M., and M. A. Kehinde. “A-4 Step Chebyshev Based Multiderivative Direct Solver For Third Order Ordinary Differential Equations.”\u00a0<\/span>Edumania-An International Multidisciplinary Journal<\/span>, vol. 2, no. 4, 2024, pp. 17\u201333.\u00a0<\/span>https:\/\/doi.org\/10.59231\/edumania\/9070<\/span><\/a>.<\/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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Statements & Declarations<\/h6>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Peer Review:<\/span>\u00a0The scholarly quality and technical accuracy of this manuscript have been confirmed through a comprehensive peer-review process conducted by experts in the field.<\/span><\/p>

Review Type:<\/span>\u00a0The journal employs a double-blind peer review model for all submissions. In this process, the identities of the authors, O.M. Ogunlaran and M.A. Kehinde, were unknown to the reviewers, and the reviewers’ identities were unknown to the authors. The review was carried out by subject experts in applied mathematics and numerical analysis.<\/span><\/p>

Competing Interests:<\/span>\u00a0The authors, O.M. Ogunlaran and M.A. Kehinde, jointly and individually declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.<\/span><\/p>

Data Availability:<\/span>\u00a0All data generated or analyzed during this study, including the numerical results and computational algorithms used to support the findings, are fully included within this published article. No external datasets were required for the validation of this theoretical work.<\/span><\/p>

Funding:<\/span>\u00a0The authors confirm that this research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. The work was completed using institutional resources and personal efforts.<\/span><\/p>

License:<\/span>\u00a0This article is published under the terms of the Creative Commons Attribution License <\/span>CC BY-NC-ND 4.0<\/span>. This open-access license allows for the broadest possible dissemination and re-use of the scholarly work, provided the original authors are properly attributed.<\/span><\/p>

Ethical Approval:<\/span>\u00a0Ethical approval was not required for this study, as it is purely theoretical and computational in nature. The research did not involve the collection of data from, or experimentation on, human subjects or animals. It adheres to the highest standards of academic integrity and research ethics in mathematical sciences.<\/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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  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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    \n\t\t\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<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

    Edumania-An International Multidisciplinary Journal Vol-02, Issue-04 (Oct -Dec 2024) An International scholarly\/ academic journal, peer-reviewed\/ refereed journal, ISSN : 2960-0006 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 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":9298,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"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"],"acf":[],"_links":{"self":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/9346","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/comments?post=9346"}],"version-history":[{"count":3,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/9346\/revisions"}],"predecessor-version":[{"id":29307,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/9346\/revisions\/29307"}],"up":[{"embeddable":true,"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/pages\/9298"}],"wp:attachment":[{"href":"https:\/\/icert.org.in\/index.php\/wp-json\/wp\/v2\/media?parent=9346"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}