Direct Solution of Initial Value Problems of Fourth Order Ordinary Differential Equations Using Modified Implicit Hybrid Block Method

Kayode, John Stephen; Duromola, M. K.; Bolaji, Bolarinwa

doi:10.9734/jsrr/2014/11953

Cited by 9 publications

(13 citation statements)

References 4 publications

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“…Nevertheless, these factors introduce an alternative to decide either to accept or reject result. This terminal result also demonstrate the functioning of the P-CB-MD were discovered to obtain an improve maximum errors than AAFO-SPIBM, AS-SCMM, DBP-CMS, DSIVP, NS-SNM, SSBM, S-SS at all convergence criteria as cited in Awoyemi et al (2015), Duromola (2016), Kayode et al (2014), Mohammed (2010), Olabode (2009), Olabode and Alabi (2013), Omar and Kuboye (2016). Thusly, it will be concluded that the P-CB-MD formulated is worthy for solving fourth order ODEs.…”

Section: Resultssupporting

confidence: 72%

“…Nevertheless, each has their benefits and shortcomings for executing them. Interested readers are invited to read Adesanya et al (2012), Anake and Adoghe (2013), , Awoyemi et al (2014Awoyemi et al ( , 2015, Kayode (2008), Kayode et al (2014), Oghonyon et al (2015Oghonyon et al ( ,2016, Olabode (2009), andOlabode andAlabi (2013) for more information.…”

Section: Introductionmentioning

confidence: 99%

“…Authors have proposed block-predictor-corrector method in the form of Adams family as situated in , Awoyemi et al (2014), Kayode (2008), Kayode et al (2014), Oghonyon et al (2015Oghonyon et al ( ,2016, Olabode (2009), andOlabode andAlabi (2013). The backward differentiation formula (BDF) is Gear's method known for implementing stiff ODEs as mentioned by Gear (1971), Ibrahim et al (2007), Suleiman (2007, 2008), Mehrkanoon et al (2010), and Zarina et al (2007).…”

Section: Introductionmentioning

confidence: 99%

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Programming codes of block-Milne's device for solving fourth-order ODEs

Oghonyon¹,

Bishop²,

Eke³

2018

Int. j. adv. appl. sci.

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Block-Milne's device is an extension of block-predictor-corrector method and specifically developed to design a worthy step size, resolve the convergence criteria and maximize error. In this study, programming codes of blockMilne's device (P-CB-MD) for solving fourth order ODEs are considered. Collocation and interpolation with power series as the basic solution are used to devise P-CB-MD. Analysing the P-CB-MD will give rise to the principal local truncation error (PLTE) after determining the order. The P-CB-MD for solving fourth order ODEs is written using Mathematica which can be utilized to evaluate and produce the mathematical results. The P-CB-MD is very useful to demonstrate speed, efficiency and accuracy compare to manual computation applied. Some selected problems were solved and compared with existing methods. This was made realizable with the support of the named computational benefits.

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Section: Resultssupporting

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Programming codes of block-Milne's device for solving fourth-order ODEs

Oghonyon¹,

Bishop²,

Eke³

2018

Int. j. adv. appl. sci.

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“…x New method, P = 5 see [9], P = 6 EXT 1.0031396535277390 1.003139653527739149 0.003125 CPS 1.0031396535277384 1 y iv − x = 0, y(0) = 0, y ′ (0) = 1, y ′′ (0) = 0,…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Recently, scholars have proposed a hybrid block methods for solving equation (1) directly in order to avoid the shortcoming in reduction method and to take the advantages of hybrid and block methods which includes overcoming zero stability barrier and generating numerical solutions simultaneously [7]. Some work in hybrid block methods can be found in [1], [2], [9], [10], and [4].…”

Section: Introductionmentioning

confidence: 99%

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

Omar¹,

Abdelrahim²

2016

Int. J. of Pure and Appl. Math.

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In this article, a power series of order eight is adopted as a basis function to develop one step hybrid block method with three off step points for solving general fourth order ordinary differential equations. The strategy is employed for the developing this method are interpolating the power series at xn and all off-step points and collocating its fourth derivative at all points in the selected interval. The method derived is proven to be consistent, zero stable and convergent with order five. Taylors series is used to supply the starting values for the implementation of the method while the performance of the method is tasted by solving linear and non-linear problems.

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Solving Fourth Order Linear Initial and Boundary Value Problems Using an Implicit Block Method

Adeyeye

Omar

2019

Proceedings of the Third International Conference on Computing, Mathematics and Statistics (iCMS2017)

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Direct Solution of Initial Value Problems of Fourth Order Ordinary Differential Equations Using Modified Implicit Hybrid Block Method

Cited by 9 publications

References 4 publications

Programming codes of block-Milne's device for solving fourth-order ODEs

Programming codes of block-Milne's device for solving fourth-order ODEs

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

Solving Fourth Order Linear Initial and Boundary Value Problems Using an Implicit Block Method

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