Continuous Fourth Derivative Method for Third Order Boundary Value Problems

Sahi, R. K.; Jator, S. N.; Khan, Nazar

doi:10.12732/ijpam.v85i5.9

Cited by 12 publications

(21 citation statements)

References 14 publications

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“…N −3 (x) then define piecewise polynomials R(x), R ′ (x), and R ′′ (x) which are also continuous on [a, b]. Hence, (2) and (3) have the ability to provide a continuous solution on [a, b] with a uniform accuracy comparable to that obtained at the grid points and can also be used to produce additional discrete methods (see Sahi et al [5]). The following theorem as stated in (Sahi et al [5]) facilitates the MDLMMs construction in (2) and (3).…”

Section: Construction Of Mdlmmsmentioning

confidence: 99%

“…In the recent time, tremendous attention has been shifted to developing methods for the solution of y ′′′ = f (x, y, y ′ , y ′′ ) subject to boundary conditions (see Awoyemi [1], Jator [2], Jator [3] ). For instance, three-point fuzzy boundary value problems discussed in (Prakash[4]); laminar boundary layer and sandwich beam problems in (Sahi et al [5]); numerical method for third order non linear BVP in engineering (Ikram [6]) are used in solving third order BVPs. Many of the methods above were solved by first reducing a higher order ordinary differential equation (ODE) to a lower order ODEs which takes a lot of human effort and computer time See Awoyemi [1].…”

Section: Introductionmentioning

confidence: 99%

“…Many of the methods above were solved by first reducing a higher order ordinary differential equation (ODE) to a lower order ODEs which takes a lot of human effort and computer time See Awoyemi [1]. This paper considers general third-order boundary value problems on the interval ∆ ∈ where y0, δ0, δ1, δ2, yN , yM are constants and f is a continuous function that satisfies a lipschitz condition with respect to initial conditions as given by Sahi et al [5].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multi-derivative Linear Multi-step Methods for Solving Third Order Boundary Value Problems

Areo

Abejide

2018

JAMCS

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Multi-derivative linear multi-step methods with continuous coefficients was derived through the block method approach using power series as basis function. Discrete scheme systems involving the multi-derivative linear methods were developed and their basic properties examined. The resulting schemes were used to solve general third order boundary value problems in ordinary differential equations without reducing it to first order. Numerical results were compared with the existing methods to show the accuracy and efficiency of the method. Results obtained show that our methods performed better than the existing methods.

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Section: Construction Of Mdlmmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multi-derivative Linear Multi-step Methods for Solving Third Order Boundary Value Problems

Areo

Abejide

2018

JAMCS

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“…In addition, Jator et al examined a case of high‐order continuous third derivative formulas for second‐order ODEs. In the same year, Sahi et al developed a fourth‐derivative method (FDM) with continuous coefficients to obtain primary and additional methods that are used to solve third‐order boundary value problems (TOBVPs). Likewise, Adeyeye and Omar suggested an HBM of order eight with the third derivative for solving second‐order IVPs of ODEs.…”

Section: Introductionmentioning

confidence: 99%

Heat transfer study of convective fin with temperature‐dependent internal heat generation by hybrid block method

Alkasassbeh

Omar

Mebarek‐Oudina

et al. 2019

Heat Trans. Asian Res.

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Purpose In this study, an implicit one‐step hybrid block method using two off‐step points involving the presence of a third derivative for solving second‐order boundary value problems are subjected to Dirichlet‐mixed conditions. Methodology To derive this method, the approximate power series solution is interpolated at { x n , x n + 2 5 } while its second and third derivatives are collocated at all points { x n , x n + 2 5 , x n + 3 5 , x n + 1 } on the integrated interval of approximation. Findings The new derived method not only performs better compared with the existing methods when solving the same problems but also obtains better properties of the numerical method. Afterward, the proposed method is applied to solve the problem of a convective fin with temperature‐dependent internal heat generation. The effects of various physical parameters on temperature distribution are also examined.

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“…The former developed block hybrid-second derivative method for stiff systems, while the latter introduced a Simpson's type second derivative method for the solution of a first-order stiff system of IVP. In addition, [12] proposed a continuous fourth derivative method for third-order boundary value problems. Following these scholars' footsteps a new generalized three-hybrid onestep fifth derivative method for solving fourth-order ODEs directly using the approach of interpolation and collocation will be proposed.…”

Section: Introductionmentioning

confidence: 99%

Generalized Hybrid One-Step Block Method Involving Fifth Derivative for Solving Fourth-Order Ordinary Differential Equation Directly

Alkasassbeh

Omar

2017

Journal of Applied Mathematics

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A general one-step three-hybrid (off-step) points block method is proposed for solving fourth-order initial value problems of ordinary differential equations directly. A power series approximate function is employed for deriving this method. The approximate function is interpolated at { , + , + , + } while its fourth and fifth derivatives are collocated at all points { }, = {0, , , , 1}, in the interval of approximation. Several fourth-order initial value problems of ordinary differential equations are then solved to compare the performance of the proposed method with the derived methods. The analysis of the method reveals that the method is consistent and zero stable concluding that the method is also convergent. The numerical results demonstrate the superiority of the new method over the existing ones in terms of error.

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Continuous Fourth Derivative Method for Third Order Boundary Value Problems

Cited by 12 publications

References 14 publications

Multi-derivative Linear Multi-step Methods for Solving Third Order Boundary Value Problems

Multi-derivative Linear Multi-step Methods for Solving Third Order Boundary Value Problems

Heat transfer study of convective fin with temperature‐dependent internal heat generation by hybrid block method

Generalized Hybrid One-Step Block Method Involving Fifth Derivative for Solving Fourth-Order Ordinary Differential Equation Directly

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