Comparison of Block Methods with Different Step-Lengths for Solving Second Order Ordinary Differential Equations

Omar, Zurni; Kuboye, J. O.

doi:10.1166/jctn.2018.7184

Cited by 6 publications

(2 citation statements)

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“…In finding the order of the block methods,the method proposed by Lambert[3] is employed whereby Taylor series expansion are used in expanding the y and f-functions and by further comparing the coefficients of h,this gives the block methods to be of order [7,7,7,7,7,7] T .…”

Section: Order Of Block Methodsmentioning

confidence: 99%

“…Due to several disadvantages found in reduction method, the direct method of solving ODEs of higher order was developed by lots of scholars which include Akeremale et al [4], Abolarin et al [5], Kuboye et. al [6], Omar & Kuboye [7], Adeyefa [8], Abdullahi et al [9], Adeniyi & Mohammed [10], Olabode [11], Adesanya et al [12], Omar & Suleiman [13] and Familua & Omole [14]. Specifically, numerical methods for solving equation (1) were proposed by Omar and Kuboye [15], Areo and Omole [16] and Mohammed [17].…”

Section: Introductionmentioning

confidence: 99%

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Numerical Algorithms for Direct Solution of Fourth Order Ordinary Differential Equations

Kuboye¹,

Elusakin²,

Quadri³

2020

J. Nig. Soc. Phys. Sci.

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This paper examines the derivation of hybrid numerical algorithms with step length(k) of five for solving fourth order initial value problems of ordinary differential equations directly. In developing the methods, interpolation and collocation techniques are considered. Approximated power series is used as interpolating polynomial and its fourth derivative as the collocating equation. These equations are solved using Gaussian-elimination approach in finding the unknown variables aj, j=0,...,10 which are substituted into basis function to give continuous implicit scheme. The discrete schemes and its derivatives that form the block are obtainedby evaluating continuous implicit scheme at non-interpolating points. The developed methods are of order seven and the results generated when the methods were applied to fourth order initial value problems compared favourably with existing methods.order initial value problems compared favourably with existing methods.

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