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

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 spa...

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Bibliographic Details
Published in:AppliedMath 2024-03, Vol.4 (1), p.320-347
Main Authors: Ahmedai Abd Allah, Salma A. A., Sibanda, Precious, Goqo, Sicelo P., Rufai, Uthman O., Sithole Mthethwa, Hloniphile, Noreldin, Osman A. I.
Format: Article
Language:English
Subjects:
block hybrid method
differential equations
equally spaced grid points
nonlinear jerk equation
simple iteration method
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Summary: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.
ISSN:2673-9909
2673-9909
DOI:10.3390/appliedmath4010017