Half – Step Implicit Linear Multistep Hybrid Block Third Derivative Methods of Order Four for the Solution of Third order Ordinary Differential Equations

Half – Step Implicit Linear Multistep Hybrid Block Third Derivative Methods of Order Four for the Solution of Third order Ordinary Differential Equations

Skwame, Yusuf

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Skwame

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Raymond

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Tumba

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Pius

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Adiku

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Lydia

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Federal University Wukari

Half – Step Implicit Linear Multistep Hybrid Block Third Derivative Methods of Order Four for the Solution of Third order Ordinary Differential Equations

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Abstract

This paper proposes a half-step third derivative hybrid block method with two cases of order four for solution of third Order Ordinary Differential Equations. Method of interpolation and collocation of power series approximate solution was used to generate the continuous hybrid linear multistep method, which was then evaluated at non-interpolating points to give a continuous block method. The discrete block method was recovered when the continuous block was evaluated at all step points. The basic properties of the methods were investigated and were found to be zero-stable, consistent and convergent. The develop half-step method is applied to solve some third order initial value problems of ordinary differential equations and from the numerical results obtained, it is observed that our methods gives better approximation than the existing method compared with.

References

6 Cites in Article

Reference Format

Oluwaseun Adeyeye,Zurni Omar (2018). NEW UNIFORM ORDER EIGHT HYBRID THIRD DERIVATIVE BLOCK METHOD FOR SOLVING SECOND ORDER INITIAL VALUE PROBLEMS.
A Adesanya,M Fasansi,M Odekunle (2013). One Step Three Hybrid Block Predictor-Corrector Method for the solution of.
A James,A Adesanya,Joshua (2013). Continuous block method for the solution of second order initial value problems of ordinary differential equation.
S Kayode,O Adeyeye (2011). A 3-step hybrid method for direct solution of second order initial value problems.
U Mohammed,R Adeniyi (2014). A Three-step implicit hybrid linear multistep method for the Solution of third order ordinary different equations.
Friday Obarhua,S Kayode,E Areo (2018). Three-step Four-point Optimized Hybrid Block Method for Direct Solution of General Third Order Differential Equations.

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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No ethics committee approval was required for this article type.

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Not applicable for this article.

How to Cite This Article

Skwame, Yusuf. 2021. \u201cHalf – Step Implicit Linear Multistep Hybrid Block Third Derivative Methods of Order Four for the Solution of Third order Ordinary Differential Equations\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 21 (GJSFR Volume 21 Issue F4).

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GJSFR Volume 21 Issue F4

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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Classification

GJSFR-F Classification MSC 2010: 33E30

Submission ReceivedMay 18, 2021
Peer Review Double Blind
Handling Editor
Accepted June 14, 2021
Published June 25, 2021

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v1.2

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October 9, 2021

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