An Order (K+5) Block Hybrid Backward Differentiation Formula for Solution of Fourth Order Ordinary Differential Equations

Yıl 2024, Cilt: 21 Sayı: 2, 113 - 132, 01.11.2024

Raihanatu Muhammad , Hajara Hussaini , Abdulmalik Oyedeji

Öz

This paper covers the derivation and implementation of the 4-step linear Multistep method of Block Hybrid Backward Differentiation Formula (BHBDF) for solving fourth-order initial value problems in ordinary differential equations. In the derivation of the proposed numerical method, the utilization of collocation and interpolation points was adopted with Legendre polynomials serving as the fundamental basis function. The 4-step BHBDF developed to solve fourth-order IVPs has a higher order of accuracy
(p=9). Furthermore, the proposed numerical block methods are employed directly to solve fourth-order ODEs. In comparison to some existing methods examined in the prior studies, the proposed method has a robust implementation strategy and demonstrate a higher level of accuracy.

Anahtar Kelimeler

Backward Differentiation Formula, Block Method, Interpolation methods, Linear Multistep Methods, Collocation Method

Etik Beyan

I Abdulmalik Oyedeji the corresponding author of the manuscript titled “An order (K+5) Block Hybrid Backward Differentiation Formula for Solution of Fourth Order Ordinary Differential Equations,” hereby declare that the work reported in this article is original and has not been previously published, nor is it under consideration for publication elsewhere. All authors have made significant contributions to the research, have read and approved the final manuscript, and agree to its submission to Cankaya University Journal of Science and Engineering. We confirm that the research was conducted following ethical standards. All informed consent was obtained from all participants involved in the study. There are no conflicts of interest to declare, and no financial or personal relationships that could inappropriately influence or bias the research. We acknowledge the importance of integrity and transparency in the publication process and are committed to maintaining the highest ethical standards in research and publication.

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