Two-Step Hybrid Block Method for Solving Nonlinear Jerk Equations

Kashkari, Bothayna S.; Alqarni, Sadeem

doi:10.4236/jamp.2019.78130

Cited by 4 publications

(2 citation statements)

References 11 publications

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“…known as Jerk equation is considered as one of the applied test problems. The exact solution for this test problem , according to [32], is given as…”

Section: Nonlinear Jerk Equationmentioning

confidence: 99%

Modified Fourth Derivative Block Method and its direct applications to third-order initial value problems

Momoh,

DUROMOLA,

KUSORO

2024

J. Math. Anal. Model.

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A theoretical order eight Modified Fourth Derivative four-step block method (MFDFBM) has been derived, analysed and numerically applied to solve multiple problems originating from Fluid Dynamics, engineering and other sciences. The MFDFBM was derived by applying collocation and interpolation techniques to a power series approximation. Further introducing fourth derivative terms at each of the collocating points yields a block method with an improved order of accuracy. It was observed that the order of the block method increases with the number of fourth derivative terms introduced into the integration interval. Numerical experiments are presented to test MFDFBM on numerical examples, including non-linear homogeneous thin film flow (NHTFF) problems and two non-linear initial value problems(IVPs). The experiments confirm the good impact of adding the fourth derivative terms, which help improve the order of accuracy of the derived MFDFBM, thereby minimising error and agreeing with analytical solution up to at least seven decimal places.

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“…known as Jerk equation is considered as one of the applied test problems. The exact solution for this test problem , according to [32], is given as…”

Section: Nonlinear Jerk Equationmentioning

confidence: 99%

Modified Fourth Derivative Block Method and its direct applications to third-order initial value problems

Momoh,

DUROMOLA,

KUSORO

2024

J. Math. Anal. Model.

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“…To determine the accuracy of SIM-BHM3, the numerical results are compared with Kashkari and Alqarni [40]. In their work, they implemented a two-step hybrid block method (TSHBM) with a polynomial of degree 6.…”

Section: On the Application Of The Sim-bhm To Solve Nonlinear Jerk Eq...mentioning

confidence: 99%

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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A Novel Method for Solving Nonlinear Jerk Equations

Akgül

2020

Lecture Notes in Networks and Systems

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Two-Step Hybrid Block Method for Solving Nonlinear Jerk Equations

Cited by 4 publications

References 11 publications

Modified Fourth Derivative Block Method and its direct applications to third-order initial value problems

Modified Fourth Derivative Block Method and its direct applications to third-order initial value problems

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

A Novel Method for Solving Nonlinear Jerk Equations

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