preprints.org > computer science and mathematics > computational mathematics > doi: 10.20944/preprints202401.0685.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 6 January 2024 / Approved: 8 January 2024 / Online: 9 January 2024 (10:44:34 CET)

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

delta-homotopy perturbation method; convergence; partial differential equation; Burger's equation; Bratu's equation

Computer Science and Mathematics, Computational Mathematics

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