3- Point Single Hybrid Block Method (3PSHBM) for Direct Solution of General Second Order Initial Value Problem of Ordinary Differential Equations

Omole, Ezekiel Olaoluwa; Ogunware, Bamikole Gbenga

doi:10.9734/jsrr/2018/19862

Cited by 13 publications

(8 citation statements)

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“…The constants parameters in equations ( 2) -( 4) are taken to be continuous functions and v fulfils the condition for the existence and uniqueness of the problem. It follows that ( 1) is a third-order ordinary differential equations with initial, and boundary conditions (3) - (4). Modeled equation ( 1) is of great importance to scientists and engineers due to its numerous usage in sciences and engineering.…”

Section: Introductionmentioning

confidence: 99%

“…The shooting method, and finite different method. The limitations of these methods have been discussed by numerous scholars [1][2][3][4]. For instance, The reduction approach have been reported by various literatures to have alot of limitations such computational burden, lots of human efforts, requires lots of time for the computation, and complexity in the computer computation which affects the accuracy and efficiency of the method in terms of error and time of execution.…”

Section: Introductionmentioning

confidence: 99%

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A Higher-order Block Method for Numerical Approximation of Third-order Boundary Value Problems in ODEs

Familua

Omole

Ukpebor

2022

J. Nig. Soc. Phys. Sci.

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In recent times, numerical approximation of 3rd-order boundary value problems (BVPs) has attracted great attention due to its wide applications in solving problems arising from sciences and engineering. Hence, A higher-order block method is constructed for the direct solution of 3rd-order linear and non-linear BVPs. The approach of interpolation and collocation is adopted in the derivation. Power series approximate solution is interpolated at the points required to suitably handle both linear and non-linear third-order BVPs while the collocation was done at all the multiderivative points. The three sets of discrete schemes together with their first, and second derivatives formed the required higher-order block method (HBM) which is applied to standard third-order BVPs. The HBM is self-starting since it doesn’t need any separate predictor or starting values. The investigation of the convergence analysis of the HBM is completely examined and discussed. The improving tactics are fully considered and discussed which resulted in better performance of the HBM. Three numerical examples were presented to show the performance and the strength of the HBM over other numerical methods. The comparison of the HBM errors and other existing work in the literature was also shown in curves.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Higher-order Block Method for Numerical Approximation of Third-order Boundary Value Problems in ODEs

Familua

Omole

Ukpebor

2022

J. Nig. Soc. Phys. Sci.

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“…Here, the correctness of the procedures is better than when it is reduced to the arrangement of first order ODEs. Similarly, [14][15][16] established a hybrid block method for the direct solution of the general second, third and fourth order initial value problem of ODEs respectively. Generalized hybrid technique for solving second order ordinary differential equations directly was also done by [17].…”

Section: Introductionmentioning

confidence: 99%

New Efficient Numerical Model for Solving Second, Third and Fourth Order Ordinary Differential Equations Directly

Abolarin¹,

Ogunware

Kuboye

et al. 2020

Gazi University Journal of Science

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Highlights• The paper focused on the numerical solution of higher order initial value problems.• Power series was used as the basis function for the derivation of the method.• The method solved second, third and fourth order ordinary differential equations concurrently.• This method satisfied the basic properties of a linear multistep method.• This method generated more accurate results than the existing numerical methods.

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“…Also, various authors such as [11,12,13,14,15,16] developed hybrid methods. This method, while retaining certain characteristics of the continuous linear multistep method, share with Runge-Kutta Methods the property of utilizing data at other points, other than the step point.…”

Section: Introductionmentioning

confidence: 99%

A Class of Irrational Linear Multistep Block Method for the Direct Numerical Solution of Third Order Ordinary Differential Equations

Ogunware¹,

Omole²

2020

TJANT

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This work considers the direct solution of general third order ordinary differential equation by three-step irrational linear multistep method. This method is derived using collocation and interpolation techniques. An irrational three-step method is developed. Taylor series and block methods are used to generate the independent solution at selected points. The properties of the method were also determined. The developed method was applied on general third order ordinary differential equations. And the performance of the numerical results of the method compared favourably with the results of existing authors in the recent literature to test its accuracy and stability.

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3- Point Single Hybrid Block Method (3PSHBM) for Direct Solution of General Second Order Initial Value Problem of Ordinary Differential Equations

Cited by 13 publications

References 0 publications

A Higher-order Block Method for Numerical Approximation of Third-order Boundary Value Problems in ODEs

A Higher-order Block Method for Numerical Approximation of Third-order Boundary Value Problems in ODEs

New Efficient Numerical Model for Solving Second, Third and Fourth Order Ordinary Differential Equations Directly

A Class of Irrational Linear Multistep Block Method for the Direct Numerical Solution of Third Order Ordinary Differential Equations

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