ONE-TWELVETH STEP CONTINUOUS BLOCK METHOD FOR THE SOLUTION OF $ y'''=f(x,y,y',y'') $

Areo, E. A.; Omojola, M. T.

doi:10.12732/ijpam.v114i2.1

Cited by 2 publications

(4 citation statements)

References 10 publications

(12 reference statements)

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“…In Table 2, we compare the maximum absolute errors of the SIM-BHM6 method with different variants of the hybrid block method [13,[17][18][19]. Adesanya et al [17] used the block method with six collocation points, Areo et al [18] used the one-twelfth multi-step block method, Skwame et al [19] used the equally spaced block method with five collocation points, and Osa et al [13] used the multi-step block method with fifth-fourth collocation points. It is evident that the SIM-BHM6 consistently outperforms the existing block methods in terms of reducing maximum absolute errors.…”

Section: Numerical Experimentationmentioning

confidence: 99%

“…They reported that the scheme can be implemented without the use of starting values or predictors, avoiding the necessity for complex subroutines method. Several other authors have utilized the equal step size procedure for solving the third-order IVPs [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…For large intervals, the SIM-BHM gave more accurate approximations than some existing BHMs, for example, those in [13,15,[17][18][19][29][30][31]].…”

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confidence: 99%

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A Block Hybrid Method with Equally Spaced Grid Points for Third-Order Initial Value Problems

Ahmedai Abd Allah,

Sibanda,

Goqo

et al. 2024

AppliedMath

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In this paper, we extend the block hybrid method with equally spaced intra-step points to solve linear and nonlinear third-order initial value problems. The proposed block hybrid method uses a simple iteration scheme to linearize the equations. Numerical experimentation demonstrates that equally spaced grid points for the block hybrid method enhance its speed of convergence and accuracy compared to other conventional block hybrid methods in the literature. This improvement is attributed to the linearization process, which avoids the use of derivatives. Further, the block hybrid method is consistent, stable, and gives rapid convergence to the solutions. We show that the simple iteration method, when combined with the block hybrid method, exhibits impressive convergence characteristics while preserving computational efficiency. In this study, we also implement the proposed method to solve the nonlinear Jerk equation, producing comparable results with other methods used in the literature.

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Section: Numerical Experimentationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Block Hybrid Method with Equally Spaced Grid Points for Third-Order Initial Value Problems

Ahmedai Abd Allah,

Sibanda,

Goqo

et al. 2024

AppliedMath

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show abstract

“…al. [22] and Taparki, Gurah & Simon [21]] Source: [Kuboye & Omar [23], Areo & Omojola [24] and Adeyeye & Omar [25]]…”

Section: Numerical Implementation Of the Problemsmentioning

confidence: 99%

The Direct Simulation of Third Order Linear Problems on Single Step Block Method

Sabo

Skwame

Kyagya

et al. 2021

AJRCoS

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In this article, the direct simulation of third order linear problems on single step block method has been proposed. In order to overcoming the setbacks in reduction method, direct method has been proposed using power series to reduce computational burden that occur in the reduction method. Numerical properties for the block method are established and the method developed is consistent, convergent and zero-stable. To validate the accuracy of the block method, certain numerical test problems were considered, the results shown that the accuracy of our method are more accurate over the existing method in literature.

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ONE-TWELVETH STEP CONTINUOUS BLOCK METHOD FOR THE SOLUTION OF $ y'''=f(x,y,y',y'') $

Cited by 2 publications

References 10 publications

A Block Hybrid Method with Equally Spaced Grid Points for Third-Order Initial Value Problems

A Block Hybrid Method with Equally Spaced Grid Points for Third-Order Initial Value Problems

The Direct Simulation of Third Order Linear Problems on Single Step Block Method

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