Laplace Decomposition Shooting Method for Solving Two-Point Boundary Value Problems

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DOI: https://doi.org/10.28924/2291-8639-23-2025-258
Published: Oct 29, 2025
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N. Alzaid, K. Alzahrani, H. Bakodah, Laplace Decomposition Shooting Method for Solving Two-Point Boundary Value Problems, Int. J. Anal. Appl., 23 (2025), 258.

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N. Alzaid, K. Alzahrani, H. Bakodah

Abstract

This research aims to present an efficient computational method for finding approximate solutions to the boundary-value problems (BVPs) of ordinary differential equations (ODEs), specifically, the class of two-point BVPs. This method is based on the combination of the shooting method with the mixture of the Laplace transform and the Adomian decomposition method. In addition, the study examined several BVPs in both the linear and nonlinear cases of the second- and third-order ODEs. For validating the suggested method, the acquired results are contrasted with the actual solutions and those of the other approximation methods. Moreover, the convergence of the proposed method to the actual analytical solutions has been noted to be very high. Additionally, this method provides the most accurate numerical results for BVPs per this study's findings.

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References

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