Direct Solution of Fourth  Order Ordinary Differential Equations Using a One Step Hybrid Block Method of Order Five

Omar, Zurni; Abdelrahim, Ra’ft

doi:10.12732/ijpam.v109i4.1

Cited by 3 publications

(1 citation statement)

References 6 publications

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“…Similarly, Abdelrahim and Omar derived a one‐step HBM with generalized two off‐steps using interpolation and collocation for solving third‐order IVPs. The following year, Omar and Abdelrahim proposed a one‐step HBM including three off‐step points for the solution of general fourth‐order ODEs. All these methods were limited to solving IVPs only.…”

Section: Introductionmentioning

confidence: 99%

Heat transfer study of convective fin with temperature‐dependent internal heat generation by hybrid block method

Alkasassbeh

Omar

Mebarek‐Oudina

et al. 2019

Heat Trans. Asian Res.

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Purpose In this study, an implicit one‐step hybrid block method using two off‐step points involving the presence of a third derivative for solving second‐order boundary value problems are subjected to Dirichlet‐mixed conditions. Methodology To derive this method, the approximate power series solution is interpolated at { x n , x n + 2 5 } while its second and third derivatives are collocated at all points { x n , x n + 2 5 , x n + 3 5 , x n + 1 } on the integrated interval of approximation. Findings The new derived method not only performs better compared with the existing methods when solving the same problems but also obtains better properties of the numerical method. Afterward, the proposed method is applied to solve the problem of a convective fin with temperature‐dependent internal heat generation. The effects of various physical parameters on temperature distribution are also examined.

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Section: Introductionmentioning

confidence: 99%