One Step Hybrid Numerical Scheme for the Direct Solution of General Second Order Ordinary Differential Equations

Adeniran, A. O.; Odejide, S.A.; Ogundare, B. S.

doi:10.12732/ijam.v28i3.2

Cited by 9 publications

(12 citation statements)

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“…The hybrid one step method for solving directly second order initial value problems generated in this paper is a accurate and efficient, b consistent and zero stable, c self-starting and requires only one grid functions evaluation at each integration step, d and can complete favorably with other existing methods [ [1], [2], [3], [4], [5], [6]] in the literature.…”

Section: Discussionmentioning

confidence: 99%

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Solving Directly Second Order Initial Value Problems with Lucas Polynomial

Adeniran

Longe

2019

JAMCS

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Aims/ Objectives: This paper presents a one step hybrid numerical scheme with one o gridpoints for solving directly the general second order initial value problems.Study Design: Section one which is the introduction, give a brief about initial value problem.In the next section derivation of one step hybrid scheme is considered. Section Three providesthe analysis of the scheme, while numerical implementation of the scheme and conclusion are inSections four and ve respectively.Methodology: The scheme is developed using collocation and interpolation technique invokedon Lucas polynomial.Results: The proposed scheme is consistent, zero stable and of order four and can estimate theapproximate solution at both step and o step points simultaneously by using variable step size.Conclusion: Numerical results are given to show the eciency of the proposed scheme over someexisting schemes of same and higher order[ [1],[2], [3],[4], [5], [6]].

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Section: Discussionmentioning

confidence: 99%

“…Many Authors such as Henrici [7], Simos [8] Awoyemi [9] Adeniran, Akindeinde and Ogundare [5], Adeniran, Odejide and Ogundare [4], Adeniran and Ogundare [2] have devoted lots of attention to the development of various methods for solving directly (1.1) without reducing it to system of first order.…”

Section: Introductionmentioning

confidence: 99%

Solving Directly Second Order Initial Value Problems with Lucas Polynomial

Adeniran

Longe

2019

JAMCS

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“…All numerical calculations and programs are carried out with the aid of Maple 16 software. x Error in [4] Error in [29] Error in [20] Error in [1] Error in our p = 4 p = 4 p = 6 p = 3 method p = 4 0.…”

Section: Numerical Implementation Of the Schemementioning

confidence: 99%

“…We consider an inhomogeneous problem [1] : y = −100y + 99 sin(x), y(0) = 1, y (0) = 11, h = 1 320 which has a solution of the form y(x) = cos(10x) + sin(10x) + sin(x).…”

Section: Examplementioning

confidence: 99%

Bernstein induced one step hybrid scheme for general solution of second order initial value problems

Ojo¹,

M.²

2020

Malaya J. Mat.

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In this paper, a Bernstein polynomial with collocation and interpolation techniques were used to develop one step hybrid scheme with one offgrid point for the direct solution of general second order ordinary differential equations. The basic properties of the derived scheme was investigated and found to be of order four(4), zero stable and convergent. The scheme obtained is used to solve some standard initial value problems. From the numerical results obtained, it was revealed that the proposed method performs better than some of the existing methods in the literature.

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“…Here, we are concerned with solutions of second order initial value problem of the form y = f (x, y, y ), y(a) = η 0 , y (a) = η 1 (1.1) where f : R × R m × R m → R m , and y, y 0 , y ∈ R are given real constants. Many scholars such as Henrici [11], Jeltsch [13], Twizel and Khaliq [16], Awoyemi [4], Simos [15], Yusuph and Onumanyi [18], Adeniran, Odejide and Ogundare [2] have devoted lots of attention to the development of various methods for solving directly (1.1) without reducing to system of first order equations. Hairer and Wanner [10] developed Nystromtype methods for (1.1) in which conditions for the determination of the parameters of the method were listed.…”

Section: Introductionmentioning

confidence: 99%

An accurate five-step trigonometrically-fitted numerical scheme for approximating solutions of second order ordinary differential equations with oscillatory solutions

Adeniran¹,

Akindeinde²,

Ogundare³

2018

Malaya J. Mat.

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In this paper, class of second order ordinary differential equation with oscillatory solutions is considered. By employing the trigonometric basis function, a continuous five-step scheme known as five-step trigonometrically fitted scheme is derived to approximate solutions to the class of considered equation. Consistency and zero stability of the developed method were proved. Stability and convergence properties of this new scheme were also established. The scheme so obtained is used to solve standard initial value problems with oscillatory solutions. From the numerical results obtained, it was revealed that the proposed method performs better than some of the existing methods in the literature.

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One Step Hybrid Numerical Scheme for the Direct Solution of General Second Order Ordinary Differential Equations

Cited by 9 publications

References 0 publications

Solving Directly Second Order Initial Value Problems with Lucas Polynomial

Solving Directly Second Order Initial Value Problems with Lucas Polynomial

Bernstein induced one step hybrid scheme for general solution of second order initial value problems

An accurate five-step trigonometrically-fitted numerical scheme for approximating solutions of second order ordinary differential equations with oscillatory solutions

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