Article
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The Delta-Homotopy Perturbation Method
Version 1
: Received: 6 January 2024 / Approved: 8 January 2024 / Online: 9 January 2024 (10:44:34 CET)
How to cite: Huseen, S. N. The Delta-Homotopy Perturbation Method. Preprints 2024, 2024010685. https://doi.org/10.20944/preprints202401.0685.v1 Huseen, S. N. The Delta-Homotopy Perturbation Method. Preprints 2024, 2024010685. https://doi.org/10.20944/preprints202401.0685.v1
Abstract
Homotopy perturbation and analysis methods have been widely used to obtain both approximate and exact so-
lutions to nonlinear problems. In general, these two methods are based on the Taylor series with respect to an
embedding parameter. Many researchers have compared the two methods and raised more concerns on the homo-
topy perturbation method (HPM) because the homotopy analysis method (HAM) contains a convergence-control
parameter ~: For this reason, in this article, a more general form of HPM is introduced as the -homotopy per-
turbation method (-HPM), which contains a control parameter : The introduction of parameter in this new
modi cation gives a better way to adjust and control the convergence region and the rate of the series solution.
We con rm through the given examples in this study that the HPM is a special case of the -HPM. The error and
convergence analysis of this proposed method are also presented
Keywords
delta-homotopy perturbation method; convergence; partial differential equation; Burger's equation; Bratu's equation
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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