A Five-Step P-Stable Method for the Numerical Integration of Third Order Ordinary Differential Equations

Awoyemi, D. O.; Kayode, John Stephen; Adoghe, Lawrence Osa

doi:10.4236/ajcm.2014.43011

Cited by 13 publications

(22 citation statements)

References 7 publications

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“…This convergence criteria (tolerance level) adjudicates whether the result is admitted or reiterated. The final results establish that MI's performance is observed to yield a better maximum errors than the AS-SCMM, AOSZ-SM, AAFO-SPIBM, FSBM, AEZ-SNM and DSOIVP as sited in [1,[8][9][10][12][13][14]. Therefore, it can be resolved that the devised method is suitable for solving non-stiff and stiff ODEs.…”

Section:  mentioning

confidence: 70%

“…Embracing [5,6,9,10,20], the consociated block methods (2) and the difference operator can be set as…”

Section: A Examining Some Selected Theoretical Properties Of Block Methodsmentioning

confidence: 99%

“…It has been proposed that the established method of solving (1) is by reduction to first-order ODEs. This technique of simplification possesses real severe hindrance which includes waste of human exertion, complication in the use of Mathematica package/computer software for coding and squandering implementation time [2][3][8][9][10][11][12][13][14][15]. Scholars have developed straight methods for approximating (1) with better results and efficiency.…”

Section: Introductionmentioning

confidence: 99%

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Block Milne’s Implementation For Solving Fourth Order Ordinary Differential Equations

Oghonyon

Okunuga

Eke

et al. 2018

Eng. Technol. Appl. Sci. Res.

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Block predictor-corrector method for solving non-stiff ordinary differential equations (ODEs) started with Milne’s device. Milne’s device is an extension of the block predictor-corrector method providing further benefits and better results. This study considers Milne’s devise for solving fourth order ODEs. A combination of Newton’s backward difference interpolation polynomial and numerical integration method are applied and integrated at some selected grid points to formulate the block predictor-corrector method. Moreover, Milne’s devise advances the computational efficiency by applying the principal local truncation error (PLTE) of the block predictor-corrector method after establishing the order. The numerical results were exhibited to attest the functioning of Milne’s devise in solving fourth order ODEs. The complete results were obtained with the aid of Mathematica 9 kernel for Microsoft Windows. Numerical results showcase that Milne’s device is more effective than existent methods in terms of design new step size, determining the convergence criteria and maximizing errors at all examined convergence levels.

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Section:  mentioning

confidence: 70%

“…Embracing [5,6,9,10,20], the consociated block methods (2) and the difference operator can be set as…”

Section: A Examining Some Selected Theoretical Properties Of Block Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Block Milne’s Implementation For Solving Fourth Order Ordinary Differential Equations

Oghonyon

Okunuga

Eke

et al. 2018

Eng. Technol. Appl. Sci. Res.

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“…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%

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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A new block method with variable stepsize implementation for solving third‐order differential systems

Rufai,

Carpentieri,

Ramos

2024

Math Methods in App Sciences

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This article presents an efficient one‐step hybrid block method (OHBM) to solve third‐order initial value problems (IVPs). The proposed method is derived using interpolation and collocation techniques of the assumed exact solution and its derivatives. The theoretical properties of the OHBM are analyzed. An embedding‐like technique is utilized and executed in an adaptive mode to improve the performance of the proposed method. The OHBM's efficiency and accuracy are tested by solving practical application problems in applied sciences and engineering. The numerical solutions demonstrate that the proposed OHBM is highly efficient and provides very accurate approximations.

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A Five-Step P-Stable Method for the Numerical Integration of Third Order Ordinary Differential Equations

Cited by 13 publications

References 7 publications

Block Milne’s Implementation For Solving Fourth Order Ordinary Differential Equations

Block Milne’s Implementation For Solving Fourth Order Ordinary Differential Equations

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

A new block method with variable stepsize implementation for solving third‐order differential systems

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